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which distribution of US interest rates is proper to use for bond option pricing?
There are a number of competing models. If you are valuing short-term options on long-term bonds, you can get away with lognormal. Otherwise you need some kind of interest rate model, no static parameter random walk will suffice.By the way, to price an option, it's not enough to know the probability distribution of the underlying at expiry, you need to know the process generating the paths to get there.
which distribution of US interest rates is proper to use for bond option pricing?
There are tons of materials and threads written on this. See the FAQ on interest rate models, or any of the half dozen or so books on the subject.