I'm prepared for a diatribe... but...
Bubbles are classicly associated with a dislocation between capital prices and rents/dividends/returns. Or:
"An economic bubble (sometimes referred to as a speculative bubble, a market bubble, a price bubble, a financial bubble, a speculative mania or a balloon) is trade in an asset at a price or price range that strongly deviates from the corresponding asset's intrinsic value."
We are not seeing that (yet) in the student housing market. Rental yields are still healthy - in general, higher than usual residential yields. So at the moment prices seem still reasonably closely linked to their current intrinsic value.
What we are in instead is a student accom development boom. If course, that boom in development mayprecipitate a big decline in rents if the demand from students for all these new units is not there. There are certainly more than enough students - but many may prefer the house share option over the slightly more sterile and more expensive student accomodation option. If that happens we will have a bust. Development will cease (and we may even see conversions out of student accom in some of the 'flexible' schemes), and capital prices will tank.
That is a real risk. I don't know what probability to put on it. But the scale of development in Cardiff is obviously increasing that risk.
But there is a difference between a "price bubble" and a "development boom". In the former, prices of an asset rise on speculation of further increases in the price of the asset. In a "development boom", new supply is added quickly in anticipation that there is strong demand for the product that will support rents. Still risky, but probably less risky than if this was all being driven by capital/price appreciation.