One method, which i used on our wool covers (which were hand woollen covers, not the BB ones) was:

a cap of wool mix in TEPID water
gently move the fibres around (to dislodge the poo)
rinse a few times

to get the water out, instead of WRINGING (as you would do for clothing), instead, double over a towel, lie it down, place your woollen object ON the towel. Now slowly roll up the towel (with the woolly in it), so the TOWEL is taking up the moisture for you.

Then, to make the cover waterproof the next time you use it, i would put the now clean woollie, into a bucket of tepid water

ADD to the bucket, the dissolved lanolin (you put a pea sized bit of lanolin, with a tiny bit of boiling or hot water, shake it in a container with a lid, so it is ALL dissolved) THEN add that to the tepid water.

leave the woolly in there for at least 30 mins

then remove from bucket, put straight onto a doubled up bath towel, and do the roll up thing again.

to dry, put item on ANOTHER doubled up towel, on a flat surface, in the shade. Under a pergola, verandah, is good, cos you get the breeze, without the sun fading your item.

that may or may not help, but oh well, putting it out there.

the baby beehinds site was pretty comprehensive last time i looked, maybe check that out, for care instructions?