I can't remember quite how close Waterloo and City is to the central line at bank, but it can be quite a walk underneath bank.
Also, getting on a train from Bank to Liverpool Street at rush hour can be anything from get there and get straight on a train (rare), to having to wait for 3 trains until you can squeeze onto one (common). They do come along about every two minutes mind.
After a couple of days you'll quickly learn where to queue though to get off at the right place, be off first, and avoid the traffic mind.
I spent six weeks doing Rush Hour London Bridge to Liverpool Street between 17:30 and 18:00 over Summer.
It was northern line from London Bridge to Bank and then central line to Liverpool Street.
Honestly, it really wasn't too bad. I didn't think I'd like the whole sardine thing, but really, you get used to it, and it's not too bad...
kd