Was this something that happened Immediately like with the British colonies or was it much more gradual due to the heavy military presence in their colonies? It just seems like colonial women are left out of much of what I've read which seems odd.
Great question! Short version: migration of Spanish women was indeed low until ca. the 1530s, with about 1.000 women leaving Spain per year. This can also be connected to the harsh conditions of life in early colonial times, especially during the military campaigns. With an increasing stability at least in the colonial centres and increasing ubranisation, female (but also male) immigration picked up, with ca. 2.900 Spanish women arriving yearly in the Americas between 1500 and 1700.
There is a lot of interesting research on women in Ibero-America. I'll have to narrow down my focus here mostly on Spanish America keeping it quite general, with some example drawn from colonial Mexico which I'm more familiar with.
In the earliest phase of Spanish military campaigns, migrants were overwhelmingly men. While expedition leaders were mostly hidalgos from the lower nobility, most of them came from the lower rungs of Iberian society. This meant that from the start there were relations between Spaniards and native women. As Susan Kellogg argues these could take different forms: Ranging from rape (often during the wars, and often as a deterring strategy), to forced marriages or non-legal unions, to marriages from which both partners could profit. It's important to highlight here that native women were not simply passive, esp. with the last example we can note indigenous female nobles who continued to hold power into colonial times. Both Spanish and indigenous elites e.g. in central Mexico saw that they could profit from dynastic unions in order to increase the new political orders legitimacy.
The early conquistadors in Mexico/New Spain also tried to legitimize or extend their holdings by marrying local noble-women. The most famous cases were dona Isabel Moctezuma's (formerly Tecuichpochtzin), the late Mexica ruler Moctezuma's most important female heir, and her half-sister dona Leonor. After fathering a child with her, Cortés had her married to another conquistador. Both sisters received important encomiendas (large territories with rights over indigenous labor and tribute), which were defended by their Spanish husbands, and later by their descendants. In these defenses before courts the royal Moctezuma's patrimony and conversion were invoked succesfully. (this paragraph is adapted from this earlier answer of mine, were I talk more about native women of colonial Mexico)
As shown in the early conquest period of the Americas there was mostly migration of European men. Especially for military expeditions women were mostly excluded. In contrast colonisation and female immigration Portuguese had a slower pace. After the initial campaigns some women arrived, with the following years bringing more immigration. Those who arrived early on often had to endure hunger and a lack of resources, but often showed courage and leadership as well. There were for example 8 women who took part in Pedro de Mendoza's ill-fated expedition in the 1530s, with one donha Isabel de Guevara surviving it and settling near Buenos Aires in 1537. Some women found themselves in the violent civil that followed conquest e.g. in Peru - this could mean that many women in that period would remarry because their husbands died in such conflicts; and would have to cope with their children's death due to conflict or disease.
The Spanish Crown as well as the church considered Spanish women as central to colonisation. They were perceived to bring iberian culture and "civilisation", and of course increase European Christian population (not my formulation, but ideas used at that time). The idea was that women should join their husbands who had already immigrated, but also to bring over unmarried women. Since usually the wives of the conquistadors and earliest settlers were usually much younger than their husbands, Spanish women would often become widows. They could inherit their husbands' encomiendas (rights to native labor), but due the patriarchal nature of Iberian law they often served only as "placeholders" for male inheritors. In addition, rich widows would come under pressure to remarry soon. Nonetheless there are cases of influential widows who refused to remarry, showing their agency, and thus continued to wield power - sometimes joining a cloister could also serve as a "way out" of remarrying. This was the case for the Estrada family of colonial Mexico, where three generations of widows from 1520-80 including donhas Luisa and Francisca de Estrada decided not to remarry in order to keep their influence and relative economic independence, going against the mores of the time (as shown by Shirley Flint).
Susan Migden Socolow in The Women of Colonial Latin America (57-58) notes the initially low female migration rates in more detail:
As early as 1498, thirty Spanish women accompanied Columbus on his third voyage to the Carribbean. The initial rate of immigration for European women was low; no more than 6 percent of immigrants were women in the 1st decade, and women were only 10 percent of all colonists who came to America in the first 30 years after conquest. It is believed, for example, that between 1509 and 1519 only 308 Spanish women arrived in America. ... Between 1509 and 1538 perhaps 1.000 women left Spain for America.
Most of those early migrants came from Seville and southern Spain, from where ships left for the Americas. Most travelled in families or as female servants.
Both Spanish men and women were not only nobles (mostly hidalgos, from the lower nobility) - the majority came form middle and commoner backgrounds, including artisans and poor people. Women and men would also come over as servants to nobles, priests or officials. Spanish women who arrived overseas could provide for passage to female relatives.
Socolow again has some more concrete numbers of the increasing immigration post-1530 (p. 62):
Over time, increasing numbers of Spanish women and children arrived in the colonies. By 1530, Spanish women figured regularly in the lists of immigrants leaving for the New World. 10 years later, European women could be found in most Spanish American cities ranging from Mexico to Asunción, and by 1550 they were a substantial presence throughout the colonies. Female immigration to America rose to 16.5 percent by 1560s as increasing numbers Spaniards, believing that their fellow settlers presented good opportunities for an advantageous marriage in America, began to import [sic] their unmarried sisters, cousins, and nieces. [Immigration] reached a high point of 28 percent to 40 percent of all immigrants by the end of the century, declining slightly by the 17th century. In the 18th c., when Spanish immigration picked up again, women constituted a mere 15 percent of the immigrant group.
Between 1500 and 1700, it has been estimated that 2.900 Spanish women arrived in America each year. Immigration of Portuguese women to Brazil was always lower. In the same time period, probably more than 100.000 Portuguese women made their way across the Atlantic, and average of about 500 per year.
The combined effects of increased immigration and birth meant that by the late 16th c. Spanish women were much more common in many Spanish American regions - although esp. in border regions were life was harder and in the Portuguese possessions their presence was still more scant. By then the first convents were also built, in part to (as mentioned) provide space for daughter who found no fitting match. Spanish men would marry Spanish women who had migrated or who increasingly had been born overseas - we can see here the beginning of creole society with its own identiy and culture distinct from the metropole. In part this was all still connected to colonial policies encouraging European immigrants to marry.
Then again, such official ideals don't grasp the complexity of ethnic and gender relations in colonial Latin America. This would be a whole nother topic, so I'll just add here that throughout colonial times Europeans were in a minority: they were greatly outnumbered first by native Americans and Africans (esp. brought over as slaves); and later by people of mixed European-native American, native-African, or European-African descent (those categories get tricky quick). The official narratives of European-European marriages did not hold up to the complexities of colonial inter-ethnic marriages and hierarchies.
So that lastly
the female population of European descent in Spanish America went from scarcity to parity and in some regions to oversupply. The rapidity with which a society of male conquistadors was transformed into one of male and settlers varied from place to place, but the transformation was usually accomlpished within 2 or 3 generations. While numerical gender parity was slower to be established in Brazil, there too the number of women of European descent came to equal that of men. (Socolow, 63-64)
Flint, Shirley Cushing: No Mere Shadows. Faces of Widowhood in Early Colonial Mexico, 2013
Kellogg, Susan: Marina, Malinche, Malintzin: Nahua Women and the Spanish Conquest, in: José Limón and La Malinche: the dancer and the dance, ed. by Seed, Patricia, 2008
Lavrin, Asunción (ed.): Sexuality and Marriage in Colonial Latin America, 1992
Socolow, Susan Migden: The Women of Colonial Latin America, 2000
Edit: added sources
I know her fate is something of an outlier, but María de Estrada was one of the first Spanish women to arrive to the new world. She originally followed her brother Francisco de Estrada there, but was shipwrecked on Cuba and spent several years there before other conquistadors arrived. She soon afterwards married the Spanish colonist Pedro Sánchez Farfán and later joined Hernán Cortés expedition to Mexico and is noted to have participated in the fighting at Tenochtitlan as a rodelera (a swordsman fighting with a sword and shield). Afterwards she and her husband were given extensive encomienda in the northeastern part of Mexico. While hardly representative of the average colonist she certainly led an interesting life.