Is that the bar you use for squats? There's no knurling in the middle, so it will slip down more easily and force your wrists to work harder. If you have access to a better bar, use it.
Chalk the back. Normal people will give you weird looks, but they'll shut up when you use 3-4 plates.
Don't chicken wing. Look up. Try to do a behind the neck press with the bar. Some use the cue "push your elbows forward", but trying to press works better for me. Do whatever works for you.
I like to have the bar lower, on my rear delts and rhomboids. You'll need more meat there, it will help a lot.
Become a better presser. Helps with holding the bar. Supporting close to twice your max bench is a bitch, so get better at pressing and your hands will be able to handle this easier.
All this should help a little. If not, show us a vid and tell us what kind of weight you use.