A recent paper looks at the connection between volatility and bubbles to see if it can serve as a signal for a coming crash. Some researchers have found a positive correlation between increases in volatility and crashes but the work has not been broad-based. The idea is simple. Higher implied volatility in a bubble market could serve as a signal of dispersion in views and suggests that the one-directional market is coming to an end.
The new research, which looks at 40 bubbles, finds no connection between volatility and bubbles. See "Can We Use Volatility to Diagnose Financial Bubbles? Lessons from 40 historical bubbles" from ETH Zurich. ETH Zurich is now the center of very interesting research on bubbles. What the authors do find is that 2/3rd of the time bubble crashes actually follow periods of low volatility. The markets do not see the crash coming and there is little dispersion of opinion. This should make any investor in bubble-type markets nervous and a reason to avoid.
I would also take a different view. If implied volatility is low before a crash, then you can buy cheap insurance at the extremes. Use the fact that volatility is not heightened to your advantage and as an opportunity if you are going to be involved with these markets.