I'll try to answer your question, sorry if it doesn't satisfy you and i'll be focusing on the Ottomans. First, we must address what exactly Bid'a is. Bid'a means innovation or more precisely, a belief or an act that is unprecedented in the time of the Prophet Muḥammad. Bidʿa is the opposite of sunna, the lifestyle of Muḥammad, a model demanding emulation. While as /u/block4 had noted this is mainly a religious and theological statement, conservative circles could use it as a pretext to reject coffee, printing, clocks, telephones, and female suffrage. However, Such conservative rejection did not always succeed. In reality, the consensus in Muslim societies as to what constitutes a forbidden and dangerous innovation (bid'a sayyi'a or bid'a madhmuma) and what is a desirable and acceptable innovation (bid'a ḥasana or bid'a maḥmuda) changed from time to time. Today’s bid'a have often turned into tomorrow’s sunna. Muslims throughout the centuries developed an extensive literature dealing with the different kinds of innovation, an attempt to distinguish between different types of innovation by means of complicated criteria. The aim was to enable a dynamic and flexible approach that could answer the changing needs of society. For example, 17th century Moroccan scholar Al-Hasan Al-Yusi challenged the notion that rational theology and logic are heretical propagated by Al-Ghazali and Muhammad Yusuf Al-Sanussi:

If it is said: Rational theology and logic are innovations and every innovation must be avoided, then we say: We do not concede that all innovations must be avoided, for some of them are commendable. Even if we were to concede this, then other sciences such as mathematics, medicine, astronomy, jurisprudence, the science of hadith and belles-lettres and the like are innovations. It may be said: But the earliest generations engaged in calculations, treatments, giving legal verdicts and relating hadith; it is only the terminology of these arts that is novel. To this we reply: Similarly, they would explicate and prove and give reasons, and there is no meaning to logic except this

So the notion of what's bid'a and what's sunna is rather flexible. Then why does the Ottoman Empire failed to adopt Printing Press and Clockmaking earlier? The answer to the former is more because of a cultural and technical reasons than a religious one, and about the latter, it has been noted that the Ottomans had made mechanical clocks for Imperial usage and the Ottoman public also adopted clocks quickly. This notion may have stemmed from a quote from the Autrian ambassador Ogier Ghiselin de Busbecq in 1592:

No nation in the world has shown greater readiness than the Turks to avail themselves of the useful inventions of foreigners, as is proved by their employment of cannons and mortars, and many other things invented by Christians. They cannot, however, be induced as yet to use printing, or to establish public clocks, because they think that the scriptures, that is, their sacred books would no longer be scriptures if they were printed, and that if public clocks were introduced, the authority of their muezzins and their ancient rites would be thereby impaired

On the printing press, the first problem is technical difficulties related to Arabic script. The rounded and connected letters not to mention the addition of vowels and punctuation marks making it a real challenge for typesetters. The first most important Arabic literature to be printed is the Venetian Qur'an, and it was a disaster. The odd typefacing was unacceptable for Muslim calligraphic norms, and it contains numerous critical errors, making it viewed with hostility from Muslim scholars. However, improvements were made in the Italian Arabic printing house and the books produced has less mistakes, albeit still with the awkward typing. Only with the invention of lithography on 1796 these printing difficulties disappeared. However, technical difficulty, as great as it may be, can be overcome in most cases if the atmosphere is ripe for the appearance of a solution. That solution may already exist but face implementation difficulties for cultural and social reasons. First, the Ottoman public has an aversion to printing because manuscript writing was held in high esteem and the preparation of fine manuscripts for elite consumption enjoyed high cultural standing. The French orientalist Antoine Galland said he came across printed books in the markets. One could purchase a printed copy of Ibn Sīna's Canon, but no one wanted it, and like other printed books, it gathered dust on store shelves. Manuscript copies of the same works were easily and quickly sold, though for a higher price than that of the printed versions. Secondly, because of said difficulties in printing, fear arose that an unintentional error in a holy text could mislead the unlearned. Handwriting can always be corrected or a single manuscript destroyed, however, printed text, which by its very nature is issued in large numbers of copies, posed the danger of an irrevocably unfixable error. Third, printing could also endanger the livelihood of thousands people making their living from the crafts of book publishing who copied plenty of books rapidly. Comte de Marsigli, writing in 1682 related about this:

Turks do not always get their works printed; but this is not, as commonly believed, because printing is forbidden or because their works are not worth printing. They do not want to prevent all the copyists whose number reached ninety thousand when I was in Constantinople, from earning their living; and this is what Turks themselves told the Christians and Jews who wanted to introduce printing techniques to the empire in order to make profits.

Now on clocks, the Ottoman Empire had paid little attention to European clocks on the 14th to 16th century because of their high degree of error. However, by the 16th century the Ottoman timekeepers had turned to mechanical clocks because their principal time-keeping devices, the sundial and the water-clock had been proven to be deficient. From the second half of the 16th century on, mechanical clocks brought from European countries such as Holland, Germany, Hungary, and France could be seen in the Ottoman world and therefore the tradition of clockmaking and clocks was not foreign to Ottoman culture. A guild of clockmakers was founded in the imperial palace, among them were two masters Hasan and Pervane whose works have survived to this day. Domestic clocks began to appear in Istanbul mansions by about 1550, and at the end of the century had apparently become quite common. Taqi al-Din described two kinds: the larger, which stood on brackets or was affixed to the wall, and the smaller, found on tables. Notably, Taqi al-Din had also constructed an observational clock which was the most accurate timepiece of its day. Some earlier scholars have wrongly taken Busbecq’s words to mean that the Ottomans had no interest whatsoever mechanical clocks, however this lack of interest had only applied to tower or turret clocks, which was indeed rare in Ottoman lands in the 16th to 17th century but this had more to do with their expense, impracticality and accuracy than with any religious qualms. However, We do not have any information as to whether further attempts at invention and development were made after the 16th century. From the first half of the 17th century, Europeans who had settled in Istanbul undertook the making of mechanical clocks. Genoese clockmakers who established a guild in Galata after 1630 supplied the necesssary clocks. From the eighteenth century onwards, European clockmakers, who noticed that the Turks had a taste for clocks, began to construct clocks for this market. As a result of mass production by the Europeans, production in Galata folded when imported clocks became cheaper than domestic-made ones. There may have been local attempts at clockmaking as we have seen in the imperial palace, but we do not know for sure.

Sources:

Science Among the Ottomans, The Cultural Creation and Exchange of Knowledge by Miri Shefer-Mossensohn

Science, Technology and Learning in the Ottoman Empire by Ekmeleddin Ihsanoglu

Time in Early Modern Islam by Stephen P. Blake

Islamic Intellectual History in The Seventeenth Century by Khaled El-Rhouayeb

"Bid‘ah" as a religious term is interpreted as incorporating something into Islam that wasn't part of it at the time of Muhammad; in other words it's viewed as deviation from what can be called orthodoxy. For example during Muhammad's time Muslims observed two religious celebrations: Eīd al-Fitr and Eīd al-'Dha. When some Muslims, centuries removed from Muhammad's time, tried to add the birthday of Muhammad in addition to these two celebrations, their act was deemed a bid‘ah.

This shouldn't be interpreted as a religious concept that's opposed to scientific innovation. There are several examples of scientific innovations that Muslims adopted. For example, Muslims used to go to the top of the minarets (of a mosque) to make the prayer call, with the invention of microphones going to the top of the minaret became a thing of the past.

I have seen the bid‘ah concept being used in polemics against Islam on multiple occasions, and sometimes people who write/speak about it clearly lack sufficient knowledge of what the concept is really about. Could you link to the article you quoted from?

Edit: Spelling