what state are you in????
Ditto on "Start applying"
On most Combination departments, the low man on the totem pols will get more (all) shifts on the Ambulance for a while so you'll get your experience easy enough.
Even on Dept's with set rotation rules you should be able to do an on shift swap easily enough if you want more experience.
Beside just going thru the application / interview process is also good practice.
Best of luck in your search.
I would recommend doing both: getting a job on a private ambulance AND start applying to EVERY department within an area you're willing to travel to.
That's what I did and I was hired on a full-time, paid department within 3 months of graduation. But I worked on an ambulance when I first started EMT-Basic school.
It's the best move I could've made.