When has a batter given himself up?

[RSturgell]

Home team at bat, bottom of 6, 2 outs and R3. Full count on B1. Pitch comes in batter swings and misses, catcher drops ball. B1 starts walking toward his 3rd base side dugout and gets 4 to 5 steps out of box. 3rd base coach is going crazy telling him to run to 1st. B1 then starts to 1st. I call B1 out and say the game is over because B1 had not attempted to run. Obviously coach is not happy and said I called the play to quick. When is the batter considered out in this situation when not attempting to run?
Oh yeah all of this in a 9u game being umpired by just yours truly. Fun times.