How soon after blasting should i prime my piece?

Immediately.depending on where your located rust can start on you project as soon as the nosle moves to different spot so its always going to be the safest bet to go ahead and prime right after blasting.  Sure, you can wait but your setting yourself up for future troubles with your project.  Any humidity higher than 86% leaves a micro thin layer of water on everything that you cant see and while its no always an option to wait on perfect weatther waiting to long just creates more buildup and starts the rusting process and just because you paint over it doesnt mean that the process stops.  It just keeps eating away out of site. So plan to prime right after blasting if possible.