This American expression seems to have originated in the car racing community, in particular the aficionados of the Indianapolis 500 race. The first citation I can find is from a report on the 1970 running of that race, in The Lima News, May 1970:
“On the ‘bubble’ is rookie
Steve Krisiloff whose 162.448
m.p.h. was the slowest qualifying
speed last weekend.
With only six spots open, Krisiloff’s
machine would be
ousted if seven cars qualified
at a faster speed this week
end.”
The qualify event at Indianapolis is known as ‘Bump Day’ or ‘Bubble Day’.
The question is of course, why ‘bubble’? The most popular theory relates to the Indy 500 and suggests that if a driver were about to qualify and then someone did a better time and pushed him down the rankings into the non-qualifiers then dreams of qualification would be dashed and his bubble would be burst.
Other possible derivations are the bubbles in spirit levels which accurately display the threshold between verging one way or the other. Another suggestion is the bubbling of a saucepan as the water is on the verge of boiling.
The Indianapolis origin is fairly well documented. The meaning of bubble is still rather speculative.
‘On the bubble’ appears to have spawned the expression ‘bubbling under’, as describing songs which are on the verge of breaking into the top twenty charts.