The answer to your question title is no.
The act of putting raw meat on a bruise comes from Hollywood and cartoons, and it usually is adopted when you have a black eye, rather than just any bruise. But what works is the cold factor of the frozen meat and not the meat itself, since cold naturally constrains blood vessels and helps reducing the swelling.
In fact, using meat could even be dangerous because you might cause an infection.
This is always strongly discouraged, for example on the page for First Aid on About.com:
Never put raw meat on a black eye. There is a first aid myth that putting steak on a black eye will help it heal faster. It will not. In fact, putting raw meat on a black eye is more likely to cause an infection (see E coli).
And also on Geteyesmart1:
[...] Despite what you see in movies or on television, you should never put a raw steak or other raw meat on a black eye. The bacteria on raw meat poses a high risk of infection, and this method of treating a black eye has no scientific basis.
A frozen bag of veggies would likely be cleaner than raw meat, but an even better solution would be using ice packs for medical use or cold compresses.
1: American Academy of Ophthalmology Launches Expanded GetEyeSmart.org, a Trusted Source for Eye Health Information. Source