No bikes from Thredbo to the top I'm afraid. Steelmesh walking tracks only.
Best rides at the top are Charlotte Pass to Rawson's Pass return and the Link Road from Smiggins to Guthega and return.
From the Thredbo side, you can go toward Dead Horse Gap and park the vehicle then ride down the Cascades Trail.
http://www.nationalparks.nsw.gov.au/...-trail/cycling
Other very nice rides can be found in the Brindabella Ranges, Namadgi National
Piccadilly Circus to Mt Coree
Piccadilly Circus to Mount Ginini or Mt Gingera.