If buses are available from Goa airport to Panaji....??
Not that I know of. Public transportation in goa sucks and that's why hiring cabs or cars is expensive. Ola and Uber too are not allowed to operate in Goa. So your best bet is trying the pre paid taxi service at the airport which may be marginally cheaper.
At one... buses are available
Airport to vasco or Madgoan then express bus to Panjim.
Walk through naval village about 1km... bus direct to Panjim.
Buses run 06.00 to 19.00.
There's also a couple of direct a.c. coaches to Panjim.. timetable online.
Thank u Shelton.