Welcome :-)
As you are on the MIDIbox site, the choice would be to build a portable MBSEQ Sequencer, which stores your drum/bass patterns (and can also be nicely tweaked for live playing). (-> http://ucapps.de/midibox_seq.html ). It is a tremendously powerful sequencer! To save money, there are also choices to build a stripped-down unit, if you just use cardboard carton and a few leftover switches and cheap LCDs, I´d say you could build it for less than 150USD in material cost (although it will then not look as nice as the unit depicted on the ucapps.de website).
Using this sequencer as a base, you can then use specialized MIDI synthesizers for the sound generation itself, e.g. a MIDI-connected drummachine or a MIDI-connected bass synthesizer. There are lots of very nice sounding units available :-), my choices for great analog sound would be the vermona drm drum synth and a moog little phatty for (monophonic) bass sounds.
Or you could use a laptop and use VSTs to create the sounds.
Greets,
Peter