It’s possible to store blood for later use.
Page 212 of the Vampire 5E core book discusses the difficulties of using bags of blood. If it comes from the hospital and has already been processed, then it can only be consumed by vampires with the Iron Gullet Merit. If it's raw, unprocessed blood in a bag, vampires of Blood Potency 2 can drink it and gain sustenance from it. It loses its Resonance after 15 minutes.
If you're drinking from stored blood regularly, you probably have the Bagger predator type (page 176), with all the benefits and drawbacks inherent thereto, including getting the Iron Gullet merit as part of the package.
You can safely draw blood using the Medicine skill.