I'm not a Swift user myself, so I'm not sure about specifics, but I guess you would start by adding bassmidi.h to your existing bridging header for bass.h?
#include "bass.h"
#include "bassmidi.h"
Regarding playing a MIDI file, you will need a soundfont to provide the instrument sounds. There are a couple available from the BASS page (alongside the BASSMIDI download). Multiple soundfonts can be stacked (eg. different soundfonts for different instruments), but if you only want to use one, then the simplest way to do that is via the BASS_CONFIG_MIDI_DEFFONT option.