The best idea would probably be that you make a list of all influencers that you want and plan to contact in the upcoming period, and then add to that list either their Instagram profile or email address they use for business inquiries. Part of them you can contact by email, but not with mass sending, if you want some results, put the effort and personalize your messages a bit at least. The same goes with Instagram DM contacting, don't do it all at once it will look spammy and you won' get many responses.