Although the dumbbells were known since the late antiquity (attested in late 1st century CE, as evidenced by a mosaic from Porta Marina in Ostia Antica), modern barbells are a relatively modern addition to the sports equipment collection, having been introduced around 1860s. This was chiefly due to the technological requirements, as a barbell needed to be made of high-quality, uniform steel to prevent breaking during lifting or dropping them from the overhead position. Until then, the mainstay of strength training were dumbbells, clubs and similar equipment. In addition to Indian Clubs, common in areas influenced by Indian and Persian culture (weights that visually resemble ancient Greek halteres were also used in China, where they were known as shisuo and Japan, where they became known as ishi sashi. Chinese martial artists also used very cheap and available burlap sacks filled with sand (chang daizi) for dynamic training similar to kettlebell swing. All of these, save for the last, were simple, compact, one-handed training equipment.
Various exercises, both dynamic (swing, snatch) and static (press) were also performed with the readily available weights commonly used for weighing bulk materials. These had usually a form of an iron ball with a handle (modern kettlebells are their direct descendants) and had a substantial mass, making them ideal for training. Depending on the sources, the first usage of such equipment for exercise dates back to the end of 17th or beginning of 18th century and was quite common in eastern Europe, possibly due to the centuries-old traditions of martial arts popular among Turkish peoples that were likely adopted from Persian and originally possibly Indian arts and methods of training utilizing various items, such as heavy maces (gada, mudgar) or shield-like weights (yekbargir), given that the earliest techniques resembling modern strenght exercises using Indian clubs are found in Arthashastra, written around 4th century BCE.
We also need to stress that the popularity of strength training and in extension, that of professional sports is relatively new phenomenon. Of course, boasting with feats of strength hails to earliest times, but regular, systematic training was until fairly recently the mainstay of the rich people whose lifestyle allowed them to use their time and energy on such pursuits. This changed only around 19th century, when the gymnastic and sports equipment started to gain more and more popularity, although it still was aimed at relatively small groups of professional performers and more affluent people of middle and upper class.
Speaking of performers, we need to say that weightlifting, although renowned as a basic physical training since antiquity, was also a permanent fixture in the showmanship, especially associated with circus shows. Given the nature of the show, a flashy movements that were visible from afar were preferable, and thus a prevalence of all movements that resulted in lifting the weight overhead with a techniques reminiscent of modern Olympic weightlifting (snatch or clear and jerk) with one-hand barbell techniques, such as bent press added to the mix. This is likely a result of natural adaptation, as the latter technique is a relatively safe and efficient way (as far as any asymmetric lifting can be considered safe or efficient, that is) to lift a weight single-handedly.
One of the reasons behind the relative late introduction of the bench press was the fact that for most of the time, although complex strength and gymnastics machines got more and more elaborate as exemplified by ones designed by Swedish physician, Dr. Gustav Zander in late 1860s, the bench was not used in a strength training in any form, meaning that the closest equivalent to said exercise was the floor press. This exercise, however, not only requires specific equipment, i.e. barbell with the weights large enough to provide adequate clearance (what before the introduction of removable plates in 1860s was not a given) but also allows for a very short stroke length due to the limitation of the movement by the floor, requiring substantial upper body strength.
The first recorded exercise similar to a bench press has been made by a Russian athlete and wrestler Georg Hackenschmidt in 1898, who, however, performed a floor press with a 333 lbs barbell. In 1900, Hackenschmidt's teacher, Georg Lurich, floor-pressed 443 pounds, although he used his abdominal muscles in the initial phase of the movements, suggesting a maneuver being a combination of a hip thrust and floor press and often referred to as a 'Pullover and Press' (not to be mistaken with 'Pullover' that bears similarity to modern 'Skull Crusher'). This exercise, easy to make while laying on the floor, was very popular throughout 1910s and 1920s and was slowly phased out in the 1930s, when the gradually stricter criteria for the performance were introduced, especially in reference to high-level competitions, including Olympic Games. The hip thrust was eventually eliminated as a valid technique in press only in 1939 in USA, to large extent due to the influence of Robert Hoffman.
This generally means that the floor press was the predominant form of the exercise, and although there are some mentions of using benches in 1930s (the first attested usage comes from Mark Berry's Physical Improvement published in 1930), the latter variant was relatively unknown until mid-1940s. Besides the ability to use other muscles, either through hip-thrusting or arching the body, floor press was far safer, as in case of a botched lift, the weights were being stopped by the floor with safe clearance between barbell and body being kept at all times. To make bench press equally safe without the necessity of using spotters, one needs to use not only rack from where the barbell is taken, but also lateral supports preventing the weight to accidentally fall on the lifter's chest or, in extreme cases, on their head. Modern bench racks started to appear somewhere around late 1940s, partially due to the tendency to isolate the movements as much as possible (and bench allows usage of legs while limiting body arching) and partially due to the greater interest in general bodybuilding. Marvin Eder and George Eiferman popularized the exercise as a one especially useful in the development of chest muscles, leading to large interest in this previously rare form of pressing.
In addition, bench press or floor press is not that intuitive as it might seem at a first glance. Modern forms of this particular exercise use isolated muscles, meaning that it uses very specific muscles to perform a relatively artificial movement. This is opposed by the 'natural' exercises that more or less mimic actual work and usually use several muscle groups at once (including 'core' muscles that help in majority of natural exercises), such as dead lift, dumbbell row, kettlebell swing, sled push etc. Regular bench press is based on a pushing motion that uses primarily pectorals, triceps and deltoids what is highly unusual in natural circumstances, where pushing primarily engages muscles of legs and back.
Furthermore, large part of strength exercises done by strongmen and sportsmen alike were usually done with the specific application of strength in mind, whether in wrestling and boxing matches or displays of sheer muscle power. Both cases required performance of advanced maneuvers, and thus highly isolated, complex exercises seemed less useful that the holistic ones that engaged many different muscle groups with the special focus being put on core muscles (predominantly large spinal and abdominal ones), very important in movement and dynamic exercises.
So, to sum it up, symmetric press is neither natural not flashy movement, and thus it has been introduced very lately. Proper bench press also required quite complex equipment that became available only in the end of the second half of 20th century. Meanwhile, bent press was largely caused by the application of heavy weights to already common one-hand lifts that required different technique, as the muscles of the arms alone became too weak to perform the exercise.
Berry, M.H., Physical Improvement, Milo Barbell Company, Philadelphia 1930.
Todd, J., From Milo to Milo: A History of Barbells, Dumbells, and Indian Clubs, in: Iron Game History: The Journal of Physical Culture, vol. 3(6), 1995.