Do TfL allow an "overdraft" of one (bus?) journey, perhaps only on
registered cards so they wouldn't have trouble getting it back? If
not, it would be worth consideration. At least one of the pre-pay
mobile phone companies allows for one "free" call in a given period (a
couple of months I think) with no credit.

If you have auto top up activated you can go into negative balance on
the bus. It is corrected once you pass through a tube station barrier.

According to their website they plan to add auto top up to bus and
trams "soon".