Bruising is a very common problem when pole dancing, especially in the beginning. Over time, your skin will get more adjusted to the activity of pole dancing causing the tendency to bruise to decrease, however bruising will most likely still happen because there are always more advanced tricks to learn : )
First and foremost, it's important to be sure you are controlling your movements with proper form and executing them with control; leaning to properly control your momentum. This allows you to avoid slamming into the pole accidentally. Never push your skin or body into pain, give it time to adjust before pushing harder.
For existing bruises, my favorite topical remedies are Arnicare and Rescue Remedy cream combined together.
If you are just an easy bruiser like me, then taking an internal herbal supplement like Rutin to strengthen your veins is a good idea (plus it will help with other things like spider veins as well).
Here is a helpful article that goes into detail about everything above and provides links to the remedies I referenced > https://polefitnessdancing.com/get-rid-stop-bruising-learning-pole-dance-home/
Hope that helps : )