Do much Bible distribution over there?
You can buy Bibles in most of the larger bookstores; there are dozens of Christian books - Bibles, concordances, writings of famous Christians - available for sale in the larger, better equipped Chinese bookstores. In fact you can even get Bible stories for children at the better bookstores in China; I know, I bought that very book for my GM's niece, at the Shanghai Book Mall (something like 6-7 floors of books - a HUGE bookstore).
Possessing or distributing Bibles won't get you into trouble; it's doing so with Bibles not taxed/declared. Of course, that's true for just about any item as well.
For that matter, I've even bought domestically printed Mandarin translations of Milton Friedman's classic Capitalism and Freedom - something you'd think would be even more forbidden in China!