A couple spiders doesn`t sound like a plague, and I also don`t think it could be them that bit you. Does rather sound like bed-bugs - they are very sneaky. You never see them, or feel them - they travel on the bedlinen and just lean down and bite you!
And they are very tiny, flat, and fast!
If you ask at a Droggery for a good spray for them, (I have seen sprays for disinfecting for insects/hygiene purposes, like in hospitals) do your mattresses, all the bed, in all the cracks and crevises, check behind pictures, all furniture. And wash all the linen and duvets in not less than 60c.
So, spray, then vacuum, while all the linen gets washed.
In winter when it snows and temps get below freezing - it`s a good idea to put your mattress and duvet outside to freeze, that will kill off any eggs or whatever.
If you have any fluffy dolls .....
.....wash them too, or freeze them.
Good luck, and maybe others have better solutions for you to try.