Thanks for your question.
Bruising is individual, and is also related to the location, technique, medicines, and other factors. Bruising happens when small blood vessels are damaged -- either nicked by the needle going in, or bursting from the pressure of what's injected. The blood in these vessels leaks into the surrounding tissue and leaves you bruised. Certain medicines such as Aspirin, Advil, etc. will cause these damaged vessels to bleed more and lead to greater bruising.
To minimize this, pre and post icing will definitely help. This will constrict the vessels so that if they are damaged, they won't lead to too much bruising. Avoiding Aspirin and Ibuprofen 1 week before and immediately after your treatment is also a good idea. Firm yet gentle pressure at the site of injection will also limit your bruising.
Some have advocated Arnica montana as a pre-treatment and post-treatment medicine that will minimize your bruising. The location also has an impact on bruising (e.g. a procedure under or near the eyes has a higher risk of bruising than that on the cheeks / nasolabial folds). On the physician end, a gentle technique with minimal needle sticks will decrease the risk of bruising greatly.
As you can see, there are many factors that lead to brusing. Try the ice, avoid aspirin, and maybe even do the Arnica. Let your physician know to go slowly. These may all help minimize your bruising. Good luck!
Good luck!