Is it in the rules to run byes on a wide ball which the batsman leaves? So if I leave a wide ball, can I then run byes off it if the keeper fumbles, or will the byes not count?
They are explicitly not byes; quoting from Law 23.1 "Byes":
If the ball, delivered by the bowler, not being a Wide, passes the striker without touching his/her bat or person, any runs completed by the batters from that delivery, or a boundary allowance, shall be credited as Byes to the batting side.
(my emphasis) However, note that doesn't mean you can't run; Law 22.5 "Ball not dead" makes this very clear:
The ball does not become dead on the call of Wide ball.
just that they will be counted as wides, not byes. This makes a difference only to the statistics for the bowler and the wicketkeeper, nobody else really cares.