One thing to remember if you get a 6x6 camera is you're only going to get about 12 shots per roll, so you'll be doing a lot of changing rolls in alleys and doorways! It can take you by surprise the first few times as you're blasting away and suddenly nothing happens. One of the advantages of a MF SLR is that most of them have at least an interchangeable insert, so you can pre-load several rolls at home and change quickly in the street.
The RB is a magnificent camera but you might find its size and weight a bit daunting as your first medium format street camera (though there are some APUG experts here who use them for street work). I sometimes use a Mamiya 645 1000s for street. It's easy to hand hold and you can get a WLF for it and you get 15 shots per roll. Whether you can find one in your budget range I don't know; likewise (and even more so) an RB.
If your main issue is regarding bringing the camera up to your eye, there are are other ways of taking photos on the street with a 35mm camera. With a wide angle lens you can shoot from the hip and be pretty sure of getting something usable. I sometimes use a small camera (Pentax MX in my case, but there are many others) and just hold it in one hand by my side, zone focused and pre-metered, and just hit the shutter as I'm walking along. Some people have ingenious ways of hiding the camera - I'm sure you can find plenty to try. Might be worth looking into before you part with your hard-earned.