Can I get bonded and licenced for construction work if I am a convicted felon

First do you really need bonding? Is it a finicial bond, a completion bond? What type of bond. Is a place you are going to work for requires bonds ?

But yes, it is always a matter of what the cost of the bond will be.

Depends on the kind of bonding, i.e. just a non hazardous license/permit bond, probably so, don't think you will have a problem, I write these with no indemnity agreement, no credit check, no balance sheet or income statement, no references, just pay the annual premium and the bond is yours but if you are talking about construction contract performance bonding, then all of the above will be required plus more... and with good results... then it depends on your relationship with the writing agent, i.e. does he/she have other insurance for you? how long / well has the agent known you? etc.