I am a painting contractor and log home restoration specialist, I have general liability insurance, and today I had a customer ask that I be licensed and have a surety bond, a license is not required for this type of work in my county, city or state, so do I need to be bonded also?

Not unless your customer requires it. Then you need to determine if the cost of the surety bond can be covered by the cost of the job plus materials and profit. All they want is to make sure that if you don't finish the job, the insurance company will step in. Here's a suggestion. Have them buy all of the materials and they won't pay you until the job is done and they are satisfied.

They are indeed looking for piece of mind(IMO)

I am not sure of you are asking for the painting work or the restoration work,they are very different(especially in the eyes of the insurance carriers)Painting has limited dangers and liabilities,Restoration could have considerable ramifications.

Bonding where I am requires the total costs of a job to be disclosed,the actual contract in some cases.(as the carriers want to know how much they would be liable for if things went awry,or the customer made a claim,then they could limit the amount they would be liable for, varies from state to state... you know,the fine print:p)

I agree with ma0614, ask the customer to purchase all materials,pay schedule is up to you and your needs,half job/half pay,for example.

If they aren't satisfied with this,you know the routine,on to the next!

There are different types of bonds - payment bonds, completion bonds, etc. Did they specify what type they were looking for?