K.G.
When I went to work and dropped my kids off at daycare, there were three bags total: their food bag (I'm a little anal about that), their diaper bag that I restocked every day, and then my pump bag. I had an Ameda Purely Yours that was much smaller than the Pump in Style, and I loved it. Inside my pump bag, I had all the necessary parts, Medela's cleaning cloths (so I cleaned all the parts right away and never had to schlep dirty parts home), my lunch, and my paperwork. I also had a very small wallet, so that fit in one of the end pockets.
Barring getting a new breast pump that takes less space, try putting all your stuff in a total of two bags: your pump bag and your "other" bag.