Dirty money refers to income garnered by illicit means (e.g. drugs, prostitution). A common metaphor for engaging in immoral deeds in general is "to have dirty hands." Sanitizing thus refers to either money laundering or avoiding criminal liability.
A play on words. "Dirty Money" can mean money used in exchange for narcotics, but when you deal with a lot of money your hands will get dirty from residue and dirt from its past owners.
"Dirty Money" is a euphemism for monies obtained through illicit means. Our rapper here is claiming that he is often in possession of this sort of money, and therefore must "wash his hands" of it.
Despite being in prison, I'm confident that my associates in the world at large will pay the bond necessary for my release in a timely manner. My connections and ability to escape perilous situations are like fictional British special agent James Bond.