Databases under Access have "bitness" as you have noted - 32 or 64. They have the same bitness as the copy of Access under which they were built. If you are using .ACCDB files, you at least need to adjust any subroutine declarations to allow for the bitness of Access itself and then have the user perform a DECOMPILE and RECOMPILE under the bitness of their copy of Access.
If you are using .ACCDE files, you must build 32- and 64-bit copies separately, as you cannot recompile the .ACCDE files.
Note also that if this is a split database, usually the back-end files don't have built-in calls that run into the interface problems. You need to look up articles on "convert 32-bit to 64-bit Access" to learn about "hardening" the interface calls. If this is NOT a split database, you may have painted yourself into a corner as I don't think a shared monolithic Access DB even CAN be shared between 32-bit and 64-bit versions of MSAccess.EXE, the Access main program.