Depends on temperatures and the amount of water around, but I would be looking at 3 months or so, give or take a bit. More time if temperatures and rainfall are low.
Tony

Hope your gum if not one that sheds it's bark as orchids don't 'take' to these very well. I attach them to ironbarks and similar trees. I never remove the stocking as the plant and it's roots eventually cover it.
Hazel.

I had to remove some here recently that had been used at some stage to attach an elkhorn to a melaleuca, as it was beginning to cut into the tree - some tough stockings!!!!

What kind of orchid is it? I presume it is a native one.

This will depend on the orchid and even the location on the tree. I have seen may orchids growing on tres in the wild and some species prefer the eastern side as to get the protection from the hot PM sun/heat.

What species/variety and size is the orchid
Keith

Thanks for the messages. Yes, the orchid is a native and the gum does not shed its bark. I went bushwalking and saw heaps of orchids naturally occur like this. I am keeping the water up to them - without over watering and their new roots are attaching themselves. Ill check them after a couple more months. Thanks for the help!