Many bike helmets are designed well, but the standards aren't the same (see NRS link below), so some bike helmets will use materials that will not hold up well when exposed to water continuously. That doesn't mean a mfg can't make it better, just that the standard is different.
In general, the helmets that offer ebtter protection are more expensive. NRS sells kayaking helmets from $17 sale price) to $170 and you don't have to look hard to find higher priced models. A high price does not guarantee it is any better, but a low price is almost always a sign of minimal protection.
Of course, the key is to get something that is appropriate for the things you paddle. If you want to wear a helmet in Class I, the $17 helmet is probably overkill, but in beefy III+ and IV you want a helmet that can take multiple big hits without coming apart and you probably want a full face for the really creeky stuff.
I paddle a lot of Class II, III and some IV and I see too many paddlers that put little thought into what they use to protect their head. I'm not saying buy the most expensive thing you can, I'm saying that you ought to be willing to spend a little money to get better than adequate protection to avoid concussions or worse.
You could use a Hockey stick to paddle your kayak too, but just because it will work, doesn't mean it makes sense.
I don't have the most expensive helmets and my first one isn't even that cool looking, but they have taken several hits and they still have a lot of life left. If they last me 10 years, the total cost will be under $20 a year for both (one is ABS, the other is carbon fiber).