You put the bleach in the drinking water? Has it ever caused any problems for your rats?
No problems at all, in fact it's generally recommended for any automatic watering system. It keeps the slime and bacteria out of the lines. It's not something that would be necessary if you use water bottles. Water bottles would be cleaned every time they're filled and don't have standing water in them for long periods of time. Just make sure you use the smallest useful amount, I generally add about 1 ounce per 5 gallons of water.