I'm trying to debunk a theory and this is a key point to my argument. I just need a reliable source to reference and an answer to my question. The most recent DC canon would be appreciated if it can be found. Also I would prefer references to comics over animated series.
Are you trying to debunk MatPat's theory? :D
Anyways I looked through my collection and only reasonable source I found was New 52 Batman Vol 6 - Graveyard Shift. There's a story called Tomorrow depicting lives of Dick, Jason, Barbara and Tim at the start of Batman's career five years prior to start of the New 52. Tim is on high school and from what I understood, he was so clever he actually was able to pass the test to finish the high school prematurely.
At this point, Batman was 25 (assuming MatPat had this right) and I don't know about America, but I personally finished high school in the age of 19. If Tim was smart enough, he could do it anytime between age of 15 and age of 19, leaving him 10-6 years younger than Batman.
There are some issues with DC Rebirth and Tim Drake being a time paradox since Doctor Manhattan stole 10 years from everybody, but I assume that only affects relationship of Tim and Bruce and not affecting the age gap between the two.
Anyways, if you are really trying to debunk MatPat's theory, bear in mind he's talking DCEU here, so the comics timeline does not apply.