Do you want to adjust the tempo of 2 files and play/encode a mix of both? If so, you would indeed use a mixer for that, ie. plug both files into the mixer (with tempo adjustment enabled) and set an encoder on the mixer. I'm not a VB user myself, but the calls will be much the same in any language and could look something like this:
mixer = BASS_Mixer_StreamCreate(freq, chans, BASS_MIXER_END); // create a mixer
BASS_Encode_MP3_StartFile(mixer, options, BASS_ENCODE_AUTOFREE, outfilename); // set an MP3 encoder on it
source1 = BASS_StreamCreateFile(false, infilename1, 0, 0, BASS_STREAM_DECODE); // create decoder for 1st file
source1 = BASS_Tempo_StreamCreate(source1, BASS_FX_FREESOURCE); // enable tempo processing on it
BASS_Mixer_StreamAddChannel(mixer, source1, 0); // plug it into the mixer
source2 = BASS_StreamCreateFile(false, infilename2, 0, 0, BASS_STREAM_DECODE); // create decoder for 2nd file
source2 = BASS_Tempo_StreamCreate(source2, BASS_FX_FREESOURCE); // enable tempo processing on it
BASS_Mixer_StreamAddChannel(mixer, source2, 0); // plug it into the mixer
// set tempos/etc here
BASS_ChannelPlay(mixer, 0); // start the mixer
...
BASS_StreamFree(mixer); // free the mixer (and encoder due to AUTOFREE)
BASS_StreamFree(source1); // free the 1st file stuff
BASS_StreamFree(source2); // free the 2nd file stuff
Please see the documentation for details on the mentioned functions.