I need to know how do I go about getting my cleaning company licensed and bonded in the state of Maryland?

Licensed, you go to the city hall and get a business license

Bonded? Do you need to be bonded ? Does a customer require it. Do you want to bond some of your employees handling your cash?
But many insurance agencies sell bonds

And you did not mention insurance?

If you are asking about residential cleaning, what I found below is from the following site in Maryland. BLIS - Case Studies

Cleaning Services

In order to start a residential cleaning business, follow the steps for How to Start a Business in Maryland. Be sure to check with the Clerks of the Circuit Court in your county to find out if a business license is needed.