How should I bring an old bagpipe back into service?

Do not ever blow into old drones until they have been thoroughly oiled.

The dry, often rough bores of older pipes will rapidly absorb moisture from your breath and then crack or split. This is particularly true of blowsticks and blowstick stocks. Old sets which are just being brought back to service after a long period of disuse should be oiled to prevent cracking.

Apply mineral oil to ALL the internal surfaces including blowstick and stocks until they retain a sheen over the entire surface for at least 24 hours. This may mean oiling them every day for two weeks prior to playing them the first time. The oil treatment is not permanent, but it will slow down the rate of moisture uptake into the wood and allow the wood to become slowly equilibrated from inside to outside without building up internal stresses and cracking.

Once you have that sheen, play the set 10 minutes per day for next three days.  Swab it an re-oil when you are done each day.  For the next week play it at least 10 minutes per day and up to 30 minutes per day.  After that - anything goes.

 Once the wood is humidified from the inside to outside, there is no real risk of cracks forming and the other effects of the oil will go away after about six months anyway. Any attempts at speeding up this process may result in cracking.

For what it's worth, a really dry pipe will continue to humidify, with additional playing every day or two, over the course of about six months.  Don't make dimensional alterations to drone receivers, unless they are really bad, or make other alterations for the first six months.