Check your phonebook or search online for a party supply store. I bought a couple plastic faux-crystal punchbowls a couple years back for under $10 each.
If you have room in your freezer to make blocks of ice this is the best way to keep your punch cold without all the dilution you'll get from ice cubes. I have a couple medium-size plastic, bowl-shaped containers that worked perfectly. It took about 24 hours for the water to freeze so plan ahead.
Depending on what you have put in the salad bowl (dressing w/ garlic or other strong flavorings), the punch might take on some of those flavors as the wood is porous. Yes, also agree that letting punch sit in the bowl for an extended period of time might cause it to swell and possibly crack/split.
If you don't mind ruining the salad bowl, then you're fine.
A large glass salad bowl w/ a ladle would work. Also, since it's after the holidays, you may be able to snag one cheap. Another idea might be a soup tureen. Or, depending on the amount you need to serve, you could always rent a punch bowl.