Hi-
I'm a student at NYU and have spent a lot of time in Bellevue. I certainly wouldn't say the scut requirement is "minimal," but it's not overwhelming. You will occasionally have to draw your own labs or do patient transport, but not frequently; you do end up doing all your own blood cultures though. What I found hindering was not so much the typical scut (labs, etc) but the aggressive follow-up needed to get studies done for patients. You need to follow most orders for tests with a phone call or two. As a very busy city hospital with limited resources, there are sometimes frustrating waits for high-demand studies or procedures. This can try your patience at times.
All that said, I think Bellevue is a tremendous place to learn medicine, and in just the few years I've been around the place, huge strides have been made in improving the services. There is pretty reliable phlebotomy service for routine labs, and nurses cannot call you for IV placement unless their managers have tried and failed. The PD has made a huge commitment to improving the ancillary services, and I expect they'll continue to get better.
Bottom line, if you feel a sense of purpose in taking care of the patient population at a place like Bellevue, I wouldn't let a little extra scut dissuade you. I've not seen too many other places, but it's hard to imagine a better experience in caring for the underserved. If you feel passionately about this population, I really don't think you will mind Bellevue's inconveniences.