Mixers and sound systems are designed to accurately produce the signal that is applied. Bass/guitar amps are designed to add signal strength through a pre amp and make it sound like a bass or guitar. You are comparing apples and oranges.

BIAB should sound great via computer plugged into studio monitors or a good PA. If it doesn't sound good something is wrong with the PA or you have a poor sound card. My goal is to have my PA sound as good as my studio monitors and it does. I use a Samson 500 watt all in one stereo rig that weighs 50 pounds for everything (mixer/amp plus 2 cabinets). This PA will run everything unless you are playing a really large venue. I would not hesitate to play my bass through this rig - it has more power than my bass amp. For good guitar sound you would need a guitar pre/effectrs pedal. Think of the PA as your studio monitor - designed for power and greater coverage.

Try your existing rig with some modern PA speakers and you will be pleasantly surprized. I suspect that Bose doesn't match up well (impedaqnce full range flat response etc) with the Yamaha. I also own the Yamaha 500 watt system and it sounds great through good speakers. If this doesn't work get a decent sound card.

We quit caryuing the PC years ago and mix everything down to a MP3 player that fits in my shirt pocket. The sound is as good or better than the headphone out of your PC.