I would say at first sit back and wait for sitters to apply. This is because sitters looking will be actively looking and so are likely to find you if your listing meets their criteria, location/pets/length of stay etc. You have a far higher chance of securing a sitter this way.
If, after a week or so you have had no applications then it may be a good idea to be more pro active and start to send out some private invites. Ideally to sitters that have 'liked’saved/loved your listing in the past or you could also do a search of local sitters that you feel may be a good fit for you. Some of these may not be actively looking at the moment but an invite from you might be enough to get their interest.
It is also a good idea to add your listing to your forum profile so that sitters on this forum can take a look, and maybe even offer advice on how you could improve it if necessary . details of how to do this are on the link below.
Good Luck