I have a 240 hot tub but no 110 close. I was thinking about running a line to the hot tub controls and use 1 leg of 240 circuit to make a 110 outlet. Bad idea?

As long as there is a true neutral and a ground at the hot tub, which I am sure there is, and you protect the outlet at the hot tub control with a 15 or 20 amp circuit breaker or fuse, and install the GFI outlet between 5 & 10 feet away from the tub, and the size feeder to the hot tub can handle the added load,there is no other restriction.

Each hot tub installation requires an conveinence outlet no closer than 5 feet to the tub, and no more than 10 feet away.

If the cable for the hot tub was pulled, why could a 120 volt cable for an outlet not be pulled?