To be realistic Rockabilly can be played without a Tremelo arm on your guitar look at Johnny Burnette Rock and Roll Trio using Telecaster and acoustic guitars.
Did you know you could purchase two different size springs for your Bigsby tremelo arm? I bought the shorter one but am thinking I should get the larger as size and tension definitely matter when you are tremelo barring.
I have two guitars with Bigsby tremolos a Gibson ES-175 that I put the Bigsby on myself after ordering it online - I drilled three tiny holes in the bout just above where the strap hole goes and I haven't looked back since but I play it often, its not for looking at only. This is almost my favorite guitar practically. ES-175's rock!
The other guitar I am lucky enough to possess is a, these days relatively rare, Gretch Nashville Chet Atkins with a factory installed Bigsby. Its the one with the painted on Florentine 'f' holes. Its a time walk and still plays and sounds great. It has issues like flaking binding.
The other guitar I have with a Bigsby-esque chrome like tremelo is a Duesenburg TV Outlaw (love that name - don't know what the TV part means exactly). This is a Korean made guitar and its semi-semi acoustic.
It only has one F hole and one chamber. It does have a peach of a Tremelo arm however that takes up more room than a Bigsby but after just looking I see that's because it has more coils in its spring than the other two guitars above do. It doesn't go out of tune. It also has a P-90 pickup in the neck position and that's the 2nd main reason bought it. P-90's are fun.
“If you’re listening to a rock star to get your information on who to vote for, you’re a bigger moron than they are.”
― Alice Cooper