According to Pottermore, the International Statute for Secrecy was not enacted until 1692. Up until that point, the Magical world and the Muggle world were not separate at all. It was at that point the Muggles first began to be highly suspicious of magic in general, so in order to maintain peace, the Wizarding world went into hiding. From the date of the Statute for Secrecy, we can clearly see a sharp decline in the Wizarding world's technological advancement. Even during Harry Potter's time in Hogwarts (1991-1998), Wizarding technology has a distinct early Industrial Era quality to it.
While the Wizarding world is separated from the modern world, there are always going to be certain individuals who are more forward thinking than others, being willing to borrow and improve upon Muggle technology. We see plenty of instances of post 1692 technology being adopted by the Wizarding world: Steam engines (1712, improved in 1769), steam locomotives (1814), cameras (1826) and film (1885), printing press made newspapers (1814), cars (1886), motorcycles (1885), modern indoor plumbing (early 1800's), and radio (1920's). One such instance that is key to understanding Wizarding use of Muggle technology is the Hogwarts Express. It is an enchanted Muggle Steam Locomotive, and has been employed by the Wizarding World since 1936. It was installed under authority of Minister of Magic Ottaline Gambol to solve the problem of secretly getting students from all over Britain to Hogwarts. When it was installed, many Wizards were indignant of the idea of using Muggle technology, but they were quickly silenced by Ms. Gambol's insistance that "students either rode the train or did not attend school." The Wizarding community is led by the Ministry; if the Ministry decrees that something will be done (widespread adoption of a Muggle technology), it will be done.
Another insight into the Wizarding community's view of modern technology and changes can be found in the Pottermore article on Measurements. J. K. Rowling wrote:
Just as British witches and wizards do not use electricity or
computers, they have never turned metric. They are not governed by the
decisions of the Muggle government, so when the process of metrication
(switching to metric measurements) began in 1965, witches and wizards
simply ignored the change.
Witches and wizards are not averse to laborious calculations, which
they can, after all, do magically, so they do not find it inconvenient
to weigh in ounces, pounds and stones; measure in inches, feet and
miles; or pay for goods in Knuts, Sickles, and Galleons.
The implication of this being that the Wizarding community does what they see as needed. Something like a Muggle newspaper was deemed very useful, so the Daily Prophet was founded. A method of moving a large group of students all at once was needed, so a Muggle steam locomotive was adopted. If some Muggle technology is seen as "not terribly useful," then it is simply ignored.
The Hogwarts Express was never made to be a bullet train both because England is fairly small, and because waiting a few hours on a train ride was not deemed inconvenient enough to warrant the upgrade. Also, bullet trains and even modern three rail electric trains run on electricity; magic interferes with electricity, they'd never work properly.