I can't speak to the overheating issue, but there are three different types of heat transfer to consider:
Conduction occurs when two things are touching. The hot water will touch the tub the tub will touch the insulation etc. This is measured in R-Value, the bigger the number the better. Mass insulation like styrofoam, fiberglass batts, Rock Wool, or polyurethane foams are generally used to slow down this transfer.
Convection is when there is an airflow, so if the pump is vented it will actually cause heat to move because of the air that it blows. The way to stop this transfer is with a thin membrane so that the airflow is blocked. Any kind of film will do, but in a spa, I don't think that this is a big issue.
Radiant heat transfer is an electromagnetic transfer. All things that are warm emit this type of heat. An example is your microwave, the sun or our bodies. This type of heat travels in a straight line and travels at a speed of, you guessed it, light. The way to block this type of transfer is with a reflective surface like aluminum. It doesn't matter what you use behind the foil, so bubble, fiberglass, OSB etc will all work just as effectively. Foil should be facing towards the heat. Some manufactures will use foil on both sides (marketing gimmick), but you only need it on one side. It should also be taped with foil tape, if you are taping it on the foil side, but you can use a Tuck tape if you are on the opposite side.
I am going to guess that about 75% of all of the heat loss in a spa is due to radiant heat transfer, so it is important to address this issue first. Mass insulation will only help with the conductive heat transfer.
Heat always goes to cold, contrary to the popular belief that heat rises. So if the ground is cold, you had better insulate the bottom.