I went in May last year and the roads were fine. I had one day when it started snowing whilst out on the road, but I managed to drop down the mountains and out of the snow without any real problems. I didn't make it as far North as I wanted to though as the weather up towards Nordkapp was not looking too good at the time! I would go back at the same time of year as it means you get to see the mountains covered in snow but without the risk of roads covered in snow! It does get a bit chilly inland and up the mountains though, so make sure you have plenty of warm kit - I ended up wearing many layers while I was on the bike!
Cost wise, it is expensive and there's no getting away from that. If you have a tent, then take it - there are some excellent campsites there, but depending on when you go, you probably won't want to be camping once you get too far North due to both the cold and the fact it doesn't get dark at night! Hostels are a good option in the cities if you don't mind sharing a room (although some offer reasonably priced private rooms). In Norway they tend to be used as much by businessmen as they are by backpackers so they tend to be quite clean and modern.
As I'm sure you're aware, beer is expensive. Buying a can of beer in a supermarket costs the same as a pint in a pub over here! In bars, the cheapest pint I found was just over a fiver, and often they are closer to a tenner, so drinking isn't really an option! Food is also a little pricey, but nowhere near as bad as alcohol! I actually found that a good steak in a pub tended to be pretty good value compared to many other things on the menu! If you're camping, then make sure you take a stove and cook for yourself when you can to save a bit of money.
Anyway, I hope all of that helps and if you have any questions let me know and I'll try to answer them for you!
