A wire is a thin piece of metal in the form of a thread, made of gold in this case (I think you call this the 'direct' meaning).
Bent double in this context means to twist something back on itself. If you imagine bending a straight line '|' to resemble something like 'J' or 'U'. In this case it was done to prevent the person's tongue catching on the wire.
Another context for 'bent double' is when someone laughs, 'He was bent double with laughter'. That's where you bend forward towards the ground because you find something really funny.