Hi Becky,
Apologies in the delayed response. One tactic that you could use is to lay them out for 24-48 hours, as you mention, and most of the bugs will crawl out. Or you can gently spray them down/rinse the flowers in the sink and then lay them out for 24-48 hours to dry somewhere with good circulation and the likeliness they will dry well.
If this still doesn’t work, you could do a gentle spray bottle of some slightly soapy water fist, leave this for 8 hours, then rinse and lay out to dry.
Good luck!
Warmly,
Benna