Not sure if it would help the situation, but you could try attaching a rod to the light switch (I've seen this at a friend's house so their child could reach the switch). This will only work for the kind of switch that sticks out of the wall, but you basically drill a hole into the switch (from side to side) and then put a metal ring through it and attach a rod (my friend's used one from a set of blinds). This way their child could grab the rod from below and use it to push up or down to turn on and off the light switch in the bathroom.
As I type this, I'm thinking a simpler (but more wasteful) solution is that you could put a small lamp in the bathroom to leave on over night. Just place it in a place where it couldn't get knocked into the sink if your daughter uses the water.
Sorry I couldn't help with the actual training part, my daughter is only 4 months old, so I haven't covered that ground yet. :)
Good luck!