Especially since payload of Tu-160 is much smaller than B-1B and supersonic capability it can provide works only on very short distances - it's not for delivering bombs faster, more for running away from fighters.
That's the thing: original plan was to make Tu-160 capable of sustained supersonic flight, to actually get bombs (X-15 missiles - Russian clones of SRAM) - to the target faster. That didn't work out.
