The bridge allows buses to travel from many points around Croatia (including daily buses from/to Zagreb and Rijeka) to access the town.
Otherwise you can fly into Rijeka Airport nearby, or just drive across the bridge.
There is a bus service from Rijeka to Krk town.[http://www.autotrans.hr/Home.aspx?PageID=11]
By foot! All within walking distance, and gives you time to explore everything.
There's a youth hostel in KRK [http://www.hihostels.com/dba/hostel021005.en.htm]. It is pretty run down though and you cannot lock the toilet and shower doors! The location is excellent though and you won't get a cheaper bed. One night in a 3-4 bedroom dorm is around 117 plus tax and a "registration fee" so it sets you back about 150 Kuna. The place used to be for over 55 people, the owner has had registred it for 24 guests only so you currently will find half of the rooms locked and taped up by the tax office.