The variables on the stack are the most efficient after registers, so you are right that a local variable should be kept into a register if possible, otherwise in the stack, and only then in other places (e.g. if it is too large for the stack).

However, when writing in assembly one must pay attention that at least RBX, RBP and R12 through R15 must be preserved by any function (on Windows also RDI and RSI must be preserved).

So in your code you should not use RBX, but a volatile register, e.g. RDX or RCX. If you would insist on using RBX, it would have to be saved and restored.