I've been doing a bit of research on the hat worn by Bonehead in Beach Blanket Bingo (and apparently other Beach Party movies). The R.F. stands for Rat Fink - a character created by artist and custom car creator, Ed 'Big Daddy' Roth.
Rat Fink was the 'anti-mouse' to Disney's Mickey Mouse who Ed Roth apparently hated with a passion. The hat, which Roth dubbed a 'Hillbilly Crash Helmet', apparently became a bit of a surfing and hot-rodding icon.
I discovered most of this information from the docmentary Tales of the Rat Fink which gives the background and history of Hot Rod culture and Ed Roth's part in it.
The documentary also credits Ed Roth with inventing 'the tshirt with a message' when he began drawing some of his monsters on tshirts. Some of these can be seen in the surfer movies such as the Surfink tshirt Bonehead wears (seen below). You can buy some of these designs from the Big Daddy Roth site.
Fantastic box art for the Ed Roth designed Surfite model car
The Surfite can be seen behind Annette Funicello in this scene from Beach Blanket Bingo