Here's the setup: I have a drip system for my plants that's run on a timer attached to my outside hose spigot. The spigot is constantly on, but for about 12 hours a day the timer is closed and no water is flowing through.
Is there a danger of pressure buildup from leaving the faucet on with nowhere for it to go? Will my water bill go up astronomically?
As long as the attached timer is shut off and no water is flowing the pressure in the water line will be no different than what it would be when the spigot is turned off.
You water bill will reflect how much water that you actually use. The only way it could go up astronomically would be if the timer broke off the spigot or failed in an open mode where water was allowed to flow freely from the spigot for long periods of time.
In the past i've had two hose spigots seize up when left open all summer, relying on the nozzle on the end of the hose to control the flow. I'd recommend that you exercise the spigot valve regularly to guard against this.
Depending on the details of the hose setup, things can be stressed by the cycling on and off of pressure (due to the timer) and allow creeping. This is worse in hot weather when plastic hose softens, at least when there's no flow of cooling water.
I saw a fountain from my neighbour's setup when their hose escaped from the back of the fitting. Luckily they hadn't locked their gate, because they were away for a fortnight and I could shut it off before the bills got too high.
