Because if you are both non-Germans it will not matter - right? I assume you a re from the US as you use the word dating?
I agree fully with Jools in 12, "dating" as a concept does not exist here, except perhaps in US-influenced TV dating playing hard to get. There are some rules however, which are ususally considered when you go out with someone especially the first time.
As Jools wrote - if you can still work with him if he turns you down, I don't see why not. This I would say is a major cultural difference to when you go out with a man from the US - I would say most men and women singles lauingen are used to splitting the bill equally unless it is already a special dinner or you are married or at least offer to pay next ime around and come true!
I think most men I know would think you a leech if you continued to let them pay for your drinks and meals. Or they might consider that you "owe" them favours Even people who say "no, no I will get it" will be pleased if you do get the bill every other time, and most people I know consider it a serious breach of good conduct to never pay a round.
Again I completely agree with Jools - expecially if it is a colleague be cautious. I should add, that depends so much on the person, there really are no patent answers to this question!