I have a theory about this. Probably some economist has thought of it before now, but if so, they're being fairly quiet about it. My theory is this: the distribution of gains and losses is skewed. There are frequent small gains, and much rarer large losses. So on average, we have a market rising slowly, but if we eyeball the chart, what we see is runs of steady gain punctuated by catastrophic losses.
So how can we use this to exploit a stock market bubble? Very simply: avoid them. Yes, on any given day you can make a profit, but that's almost exactly balanced by the small chance of a catastrophic loss.
In fact, beyond some arcane and complex risk management stuff, there's no reason to "play" the stock market on a day to day basis. Choose some stocks that look good in the long term, or better yet an index fund, and leave well enough alone. By the time you realize you've made a bad decision, the stock will already be devalued to factor in that information and you may as well stick with it.