Clojure often leaves implementations to the backing platforms, and Clojurescript probably has no difference in the methods of the different numerical types.
Java does, so you'd have to fall back on that. Something like:
(defn big-or
[f & r]
(reduce (fn [acc v] (.or acc (biginteger v))) (biginteger f) r))
(defn big-and
[f & r]
(reduce (fn [acc v] (.and acc (biginteger v))) (biginteger f) r))
(defn big-xor
[f & r]
(reduce (fn [acc v] (.xor acc (biginteger v))) (biginteger f) r))
A lot of (mathemathical) operations need falling back to the platform, and this is by design for clojure. There are however libraries that are intended to abstract away the differences, and one of those for math is clojure.math.numeric-tower.
A numeric type independent implementation for bitwise operations would be a fitting pull request there.