If there is a bubble, it's most certainly not starting, it's ending. With the Fed tapering imminent, and interest rates starting to rise, there's no way that a bubble will be starting at this point. If anything, it will pop a bunch of near-bubbles, like Bay Area real estate, rent prices, stock market, etc.
There is no Fed tapering imminent. They just voted last week to keep the $85 BLN/month flowing on a 9-1 vote.
During dot.com bubble, the short term interest rate was 5%+ in 1998 and 1999, and that didn't stop that bubble. The Fed only belatedly raised rates to 6% in 2000 when the bubble went parabolic.
The Fed is always slow to raise rates, and rates are at 0%.
It could be years before we are at 2% rates with FOMC incrementing 0.25% every quarter or so, and 2% rates is still very stimulative. Right now, the Fed isn't even talking about raising interest rates. They have only been talking about reducing the $85 BLN/month $$ printing, but even that is on hold as of the last FOMC meeting where they voted 9 to 1 to not taper.
The Fed still has the pedal to the metal, and have publicly stated they do not see a bubble anywhere (just like they said there was no housing bubble back in 2006-2007). Don't get shaken out of the market just because the Fed talks about tapering its $$ printing from $85BLN/month to $75BLN/month. The current environment is still very stimulative for stocks.
If there is a bubble, it won't pop because of the Fed. It will pop after the momentum is exhausted and it collapses from its own weight.
According to Trulia's research, it will be cheaper to rent than buy in the Bay Area when interest rates hit 5.5%. For most of the rest of the country the rates would have to hit over 10% (!!!) for that to be true.
So it should prove interesting what happens then. That said, my wife and I are in the middle of (trying) buying a house here. So far, there is intense competition amongst buyers. One home we put an offer on had 19 offers total. We offered 21.5% over asking and at least 3 offers came in ahead of us.