Was the pipe busted due to freezing? I am always conflicted about dripping a faucet if we leave in the winter or if that’s asking for trouble
Not an expert here, but my brother-in-law has been Superintendent of the Water Department for almost 40 years, so we've relied on his recommendations.
In the fall, when you're done watering the lawn or using any outdoor faucets, shut the main water off and then go turn on those outside faucets and turn them on and let any water in them run out. When they are done, turn your main water supply back on. On those outside faucets, buy those cheap foam covers and put washcloths or old tee shirts inside to seal up the inside and then attach it to the faucet to prevent any air from getting in.
We bought that relatively cheap foam insulation and covered all the pipes exposed just as added insurance. It's not very costly, probably can get it for $ 2-$ 3 for each 6' section. They are slit and you put them around the pipes while taking the little sticky strip off and sealing any outside the pipe air. That insulation was good for 10-15 years.
If you have any small holes leading into the house just use the spray expansion foam which will prevent really cold air from entering.
He highly recommends leaving the water on with a trickle. As many have mentioned, leave the cabinet doors open below any sink faucet to let warm air circulate. If you suspect the dishwasher may be an issue, you can use a small space heater and place it 3' to 4' away and just turn it on low and let it heat the area for an hour or so. Dishwashers seem to be a major problem area for a lot of people because the pipes are not visible. He said, over the years, since a lot of dishwashers are setting on a small uplift or rise, and the heat from the floor will rise and not really benefit those dishwasher pipes, some have actually drilled a small hole in that riser which would allow the heat from the room or from using a heater to actually heat up those pipes which may have began to freeze.
Anyhow, not any professional advice here, just some suggestions. Sometimes we are just at the mercy of a brutal cold spell and stuff happens.