Yes, PH, my TI-92 has BesselJ(1st kind) and BesselY(2nd kind).
This is a added program, though. I don't know, some of the newer models may have it built in.
I do not own a TI, nor any calculator.
I know how they work because I helped out my classmates when I was in school. I never remember seeing "Bessel functions" on the TI, but I also did not know what they were back then so it is possible they were their and I did not know of them. Are they there?