Sorry it does only go to Airport West, but there is a bus stop next to the terminus of the 59 tram on Matthews Ave
I'm not sure about the Bus or Tram no's but I used to take bus from Airport to Airport West and get off just outside the Airport West Shopping Mall. There's a Tram stop there as well, so I just take the tram to Melbourne CBD, getting off at either Swanston or Elizabeth St. (not sure which!)....
I agree with the comments about this normal service not being publicised, and people just being misled to use the Skybus (what a big rip-off!!!).... and don't get me started on Sydney airport!!! bloody shame on the government.