It sounds like you're having trouble getting the tire bead to seat correctly near the valve, is that right?

Do you start seating the tire bead at the valve before you continue around the rest of the wheel and finish on the opposite side? Is there a lot of air in the tube when you're trying to seat the tire? Are you pushing the valve back into the rim a little to allow the tire bead to seat well below the edge? (The valve is to be without the retaining ring on the rim side for this)

It could be that the tire bead is broken or deformed too, so that you need a new tire. Does this billowing happen at the valve also when you move the tire a bit relative to the valve?