1. Ship the special "mp3-free" BASS.DLL radio42 mentioned. It's in the "mp3-free" folder in the BASS archive, and it works exactly like the ordinary BASS - however, it does not contain its own MP3 decoder. Instead, the licensed codec installed in Windows (DirectShow) is used. But you or your users won't notice, because it's all handled transparently in the background. You do not even need to change your code, just replace the BASS.DLL file.
Note that on some systems (1 out of 100 or less, in my experience), the mp3-free version is problematic, e.g. when the DirectShow MP3 codec is missing (Windows 2000 clean install!) or broken (the one that comes with BPM Studio). In that case, you should advise your users to (re-)install the latest version of Windows Media Player which will re-install a proper codec.
2. Regarding AAC, just do not distribute any problematic add-ons with your application. The user will still be able to download and install the add-ons on his own, checking all license and patent requirements first, of course
Actually there's much more to consider than just the patent fees. For example, the BASS_AAC add-on is based on FAAD2 and thus GPL'ed (by the way, where can I get its source code?), so it may not be used, not even dynamically linked, with a closed-source software.