Don't mount a bipod to a screw in type stud that has wood-screw like threads. It will work loose eventually and pull all the wood threads out of the stock
You want to use a sling swivel stud that has machine screw threads on it.
The one on the right in this pic is what you want to use.
Remove the stock, drill a pilot hole (1/16"-1/8") through it where you want the stud and then on the barrel channel side add a "Tee Nut". You can get these at most hardware stores.
It can be done with a cordless drill, a couple of drill bits, some epoxy and enough masking tape to protect surrounding stock surfaces.
A simple method is to drill a very small diameter hole through the stock at the desired stud location. Drill the recess in the barrel channel using a spade bit. Then drill the small hole out so the tee nut will fit flush at the middle. If there is any wood remaining at the bottom where the small diameter locating hole was drilled, just drill it out so the swivel threads will pass through and into the metal threads. Once the Tee Nut is fitted, just epoxy it in place using 5-Minute Epoxy.