Most bonding companies are only interested in bonding public work, not private. You may find that the contractors can not meet your bond requirement, due to the lack of appetite for privately bonded work. Also, keep in mind that the cost of the bond would be built into their bid price. In other words, you end up paying for it anyhow.
For private work, I suggest checking on their previous work and ensuring they have all required licenses up to date and without flaws.