Schedules are located behind the driver's seat, just jump on and grab one at a bus stop. There are three runs a day to North Douglas, which offers good hiking and camping areas. The ferries are another 3 miles north. Buses also run around Back Loop Road, which gets you within a couple miles of the camping and hiking areas on the east and west sides of the Mendenhall Glacier. There are cabs and shuttles.
Bikes are a great option, and rentals are available.
A number of places rent kayaks and gear as well as give guided trips. There is also an excellent, large map of area trails available. It's new this year. There are three branches of the public library, in Mendenhall Mall in the valley, in Douglas, and on the waterfront in downtown Juneau. Call around and ask for discounts.