The loss of depth of cut is dictated by the thickness of the template. The template has to be thick enough for the bushing. In my experience, expensive router bits, made by companies that specialise in routing, have longer shanks than the bargain basement router bits. Those manufacturers know that their bits might be used in a router table or with bushings and add the extra length as a matter of course.
Yonak, you can put the router bit all the way into the collet if you like, but you will have a devil of a job trying the remove it afterwards. Always better to leave a a gap at the bottom.
MJCD, I’m confused, do you not have any depth adjustment on your router? Excuse my ignorance, I have only ever used plunge routers.