Let's start by defining "bubble".
A financial bubble isn't just "asset prices are going up". Asset prices can go up because the fundamentals for the asset are good. For example, stocks can go up because earnings are good. They can also go up because bond interest rates are low, and so 4% return on stocks is now a good return.
Then next stage comes when people start buying an asset because the asset are going up, rather than because the fundamentals are good. That's the start of a bubble. It's not yet a dangerous bubble, but it's becoming a bubble. (It's dangerous to those who invest in it, but it's not dangerous to the economy as a whole.) And of course, people buying into the asset cause the price to rise further. So more people see that the price keeps going up, and buy in because they want to make money. So the price goes up some more. That's a bubble - the price is rising because people are buying, and people are buying because the price is rising.
The dangerous stage comes when people start buying the asset with borrowed money. This is dangerous because, when the bubble pops (and it always does eventually), people will lose money that they don't have. This can destroy banks, not just individuals. When it destroys banks, it can threaten the economy as a whole (think 2008, or, worse, 1929).
So: Are we in a bubble? I'm not sure that we are in the Nasdaq, given current interest rates. I'm not sure that the price is totally disconnected from the fundamentals. We could be in a bubble, though.
One metric I'd be interested it, but don't know how to get my hands on: How much borrowed money is invested in the Nasdaq (or S&P 500, or the Dow)? How does that compare to historic values?