you need to wipe the lumps off first with kitchen roll. put your hand in insoide out nappy bags as well if you don'tlike the wet feeling. then you can putll the bag right way round with sick in it and tie.
you will need to do this round the seal of your washing machine door now. otherwise you will get sick on the next load of washing.
I usually wipe most of it up, dump bedding in bath to be dealt with in the morning, in the morning shake the lumps into the bath, wipe up with loo roll and throw in toilet.
rinse the remaining sick offin the bath. do not attempt to wash lumps down the plughole, you will only have to deal with them later and it is not pleasant.
when there are just marks on the bedding, then put in the wash. there is notheing as grim as wiping sick out of the door of the washing machine.
spray bath with antibac and wipe out.
I used this method last time ds was sick and escaped the lurgy mysef.
(I am assuming you have dealt with the child first, doing the same procedure for the child really)
I try to antibac everysurface and wash hands well in the hope that the other child does not catch it. I also keep them apart for as long as possible and allow no sharing of food/drinks/utensils for a few days.