Bobert,

I would suggest painting a diluted PVA adhesive (perhaps 1:1 or 3:2 PVA:Water) applied with a suirrel 'mop' brush (if you use an aerosol it is likely to distribute the fibres, brushing with a 'mop' will tend to consolodate the surface, holding down the fibres and forming a skin.
When dry, this should hold the fibres while wrapping.

I do agree with Sorcha, get a mask with a suitable asbestos filter and I'd recommend a paper oversuit to be removed and disposed of - but then you probably know the uual precautions for removal and disposal.

Just an idea, I'm not an asbestos expert.

Walrus