Abby,
Every hospital has an " IV team" - they only do IV,and they are special trained RN nurses with usually a lot of experience. They do it quickly and professionally,they come to your place with their own "special" equipment.
Don't be shy, just tell your nurse, that you have bad veins, and you'd like the "IV team" deal with them.
You don't need to warm up your hands or those " three strikes", let them get trained somewhere else.
Just my 2 cents,been there.

Marina.