How to get phlebotomy experience

I'm a new grad (LVN, or RPN here in Canada) , and I was hired at a LTC facility.
The money is pretty good, but the responsibilities are pretty vast. I work full time night shift and I have 140 residents. Yes 140!
Most of them sleep all night, but when I have a fall or something more "critical", it's VERY stressful.
I am looking for something else as I sometimes come home crying with frustration.
I would love to be able to work in a clinic or Dr's office, but I noticed that they often ask for phlebotmony experience.
Where can I gain this experience? The hospitals here are not hiring at the moment, but do they do any sort of training for this?
Thanks for reading.
I took a 6 week phlebotomy course, but I'm not familar with what would be available in Canada.

I would recommend looking into job opportunities with Canadian Blood Services. Here in Ontario they use a mixture of phlebotomists (short course at a trade school), RPNs and RNs at their donor clinics. Part time opportunities seem to be relatively common.Canadian Blood Services - Société canadienne du sang

Thanks for the replies!And Chinook, I never thought of looking into Blood Services! I certainly will!

ask the hospitals if they have any ideas. I take new hires and put them in areas where lots of IV's are done, or lab work, for 1-2 days. They get expert fast.

I was trained as a phlebotomist but had trouble finding a job once I graduated from my program (partially because I was still in school for nursing and didn't have the greatest availability) but one way I gained experience was that I volunteered at a free clinic in their lab and did phlebotomy there. A great way to gain experience while choosing your own hours. !Chris