Haven't done a bear skull, but just did a pig skull which has to be just as greasy if not more and the Dawn dish soap simmer a few times did the trick.
Dawn dish soap and one of these bucket heaters worked for me but took about 4 months. I'd swap the water when it got murky which was probably every 2-3 days at the beginning and every other week by the end. In my sample size of 1 it's a pretty slow process but after 6 months only a little grease has reappeared at the back of the skull.
Many methods out there. I like a lot of taxidermist prefer the maceration method. I use a 1500w bucket heater. I have a thermostat on my tank and keep it just over 100 deg. It will heat a small bucket or 50 gallon tank. You don’t want it to cook, should more rot off. Takes a few days to a week for the rough clean. I add dawn to the tank after cleaning for a few days to a week. Bears are not as greasy as pig skulls. A lot of aquarium heaters and stock tank heaters don’t get hot enough.
Check out white bone creations on the YouTube, he has a lot of great info IMO. I'll be utilizing his ideas with acetone and peroxide on my two whitetails and moose when the beetles are done with them.