Fairly certain you can work with a 32 bit created db while using 64 bit but not the other way around but you'd be wise to verify that. There are things in 64 that are not in 32, so when you think about it, a 64 bit version has everything the 32 has, but not the reverse. My understanding is that you can't open the 32 bit version, rather than Access trying to figure out whether or not you used any of those features. Suggest you google (or whatever) to understand the 64 bit version differences to decide whether or not you need any of those features and see if you can convince IT if they're in the picture, to install 32 bit Office if you'll never need them. Code isn't the primary problem because code can be modified to work in both versions if there are certain API calls. If not, it's usually not necessary.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.