For filesystems like NTFS / FAT32 that don't contain the regular file attributes linux uses (the permissions, etc.), in order to run executables on that drive, you either have to mount it with the "exec" option, or you have to copy it to your linux drive first, then modify its permissions to allow execution and execute it. However, I'm left wondering the same thing as the previous poster; does real basic actually compile programs for linux, that don't need any kind of modification? I don't know anything about it, but it sounds doubtful.
Anyways, if you find that doesn't work, and you're feeling courageous, you can always try downloading wine
the windows emulator "wine is not an emulator", and see if you can get realbasic working. The long-term solution, however, if you really find linux interesting and want to develop for it, is to learn one of its primary languages; C, C++, Perl, Python, or something of the like.