Use either E-6000 glue or Liquid Nails. Make sure not to glue directly over the growing point of the base.

T. tricolor var. melanocrater as shown in the bromdex.

I use orchid wire and glue to attach a small till like that to a piece of wood. What gonzer said plus a bit of orchid wire to secure it to the base.

In this example, the piece of bark is held by the hanger and the till is glued and wired to the bark. I know, you can't see the wire, but it's there. I drill some small holes in the bark and run the wire through the holes.

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Here is a link that might be useful: tricolor var. melanocrater