Because of the roots it would probably be easier to just place that wooden basket in a bigger wooden basket to avoid tearing them up. Another option would be to soak the basket in water for about 10 minutes or so to loosen up the roots that are attached to the basket then slowly try and peel the roots away without causing too much damage. Then you could just place the plant in a bigger pot or basket.
I would try to take off as many pieces of basket as I can and then put the plant in a new wooden basket. But I'd do this next year, not this one.
Remember: Bifrenaria really DON'T like to be repotted and having roots touched. They are big but pretty fragile.