I don't think splunk does bitwise operations. After all, for bitwise operations you first need an agreement on how a number looks like in bits, and that doesn't feel splunky.
However, you can shimmy your way around that with a bit of maths. You already said how shifting is nothing else than dividing by a power of two and then flooring the result, that's the first step. Second, a bitwise and throwing out a number of starting bits and keeping all the bits after that is nothing other than a modulo operation. For instance 0x123 & 0xff is 0x23, yes? Going decimal, 0x123 is 291, doing 291 % 256 yields 35 - which is 0x23.