The closest accommodation to Belco bowl that I know of is the Belconnen Premier Inn on Benjamin Way. Its walking distance fromWestfield Belconnen and I guess if u r feeling energetic also walking distance from the Bowl too.
Not sure that it is the cheapest but certainly close.
If u r looking for cheap there is a Caravan Park on Canberra Ave (Southside Motor Village) and u can get to the bowl in about 10-20 mins depending on traffic & stuff.
Other than that, because Canberra is so small, u could almost stay anywhere u want in Civic which is only about 10 mins away from the bowl.
Hope some of this helps.
Kimberley