Hi there, If you get the train, it is only around a couple of hours time, and train from Copenhagen to Stockholm costs around EUR155
Some friends of mine took the bus from Copenhagen as it was alot cheaper - but really really long, I'm not sure of the company, maybe Swebus? Something like that.
A single from Copenhagen to Stockholm costs 800DKK. Flights might actually be cheaper. Try SAS; I managed to get my ticket from Copenhagen to Stockholm for less than 50 pounds.