I don't know - although I wasn't in London yesterday, I've found some routes surprisingly quick during previous tube strikes - I've planned to walk fairly large distances but then caught a bus once a few have passed me.
Not Fleet Street / Strand! Outside zone 1 I suspect it's rather easier too.
For the OP's question - quite often! But a bus is warm and dry. Outside rush hour, it can often be quick - so saves time. I tend to fall over if I walk and play on phone at same time...so bus means I can check work emails etc (or pokemon It's really sensitive to roadworks tho - such as the ones on Moorgate or the Tower Bridge closure etc.