Registering a business in NJ at least is easy. Goto the state page and click on business fill out the form and send in your $150. Until you get your certificate give people your business card and name. Then make it clear you're acting as a business; say "I am doing this as 'beeremoval LLC'." You must make it clear that you are acting as a business and not you personally. If any one sues. They end up having to sue an empty LLC. That's why the call it a limited liability company. The liability is on the LLC's head and if it owns nothing their is no recovery. Otherwise your personal assests (house, car, savings)are on the line. Don't lose everything over a hobby. No matter how profitable/charitable it may be.
Then you can get a bank account, insurance, and other business related stuff. Have what ever insurance you need to cover you and your equipment in case of loss (theft/damage) and long and short term disabilty and life insurance for your self. One fall off a ladder can ruin your income for a very long time, even permanetly.
Keep in mind I am not a lawyer and this is not legal advice. Just some common sense business advice.
This is good advice. LLC's are a wonderful thing.
Moonshae something else to think about, ask a few insurance companies if you can take out a 6 month policy, some allow this sort of thing. Removing bees is seasonal and it will save you some bucks.