How should we define a housing bubble?
There's no clear cut answer. The term "bubble" means different things to different people. The classic housing 2004 housing bubble paper by Karl Case and Robert Schiller explains it this way (emphasis added):
The term "bubble" is widely used but rarely clearly defined. We believe that in its widespread use the term refers to a situation in which excessive public expectations of future price increases cause prices to be temporarily elevated. During a housing price bubble, homebuyers think that a home that they would normally consider too expensive for them is now an acceptable purchase because they will be compensated by significant further price increases. They will not need to save as much as they otherwise might, because they expect the increased value of their home to do the saving for them. First-time homebuyers may also worry during a housing bubble that if they do not buy now, they will not be able to afford a home later. Furthermore, the expectation of large price increases may have a strong impact on demand if people think that home prices are very unlikely to fall, and certainly not likely to fall for long, so that there is little perceived risk associated with an investment in a home.
So where do we stand today? Well people buying homes are cite future price increases as one of the "key factors" motivating them to buy. The most recent survey by the real-estate company Redfin found that almost one third of buyers are motivated by rising prices.