I get lots of hits from searches looking for train times for the Waterloo and City line.

These are the normal times, but it may be best to check first before travelling to ensure there are no engineering works. (More relevant at weekends).

Monday - Friday

From Bank - Trains run every few minutes between 06:21 and 21:48
From Waterloo - Trains run every few minutes between 06:15 and 21:41

Saturdays

From Bank - Trains run every few minutes between 08:07 and 18:37
From Waterloo - Trains run every few minutes between 08:00 and 18:31

No service on Sundays.

For more information see Transport for London