don't get all wound up by the pisstaking replies. It's all friendly banter.
go to liverpool street in preference to bank, it's a lot closer, and buses are slow as hell through the square mile
you can get the 8 or the 388 - they both stop outside BLB on Bethnal Green Rd.
walk halfway down Brick lane to 14 bike co in the Truman Brewery - there are some nice bikes in there too - or you could walk up from Liverpool St to BLB and 14 will be on your way.
There are plenty of quiet streets around there to have a practice on.
but you'll be fine, really.
you can ride to waterloo. It's not far. follow a 26 bus from Bishopsgate. The roads are busy but slow. keep an eye out for traffic and you'll be fine.
Some proper advice: