I cannot be sure this answer is correct, but in the absence of any explanations online for 'bumping hutch' as a phrase (I tried Google and thoroughly grilled Chat GPT) I thought the best approach would be to make observations about the two words in isolation to see if there is any logical meaning that can be drawn.
I noticed that the expression "bumping Hutch" is also in the seminal work "Azz & Tittiez" by Hypnotize Camp Posse, and both uses are in the context of driving a car. Further, I saw that the word 'Hutch' is capitalised in some lyrics listings for these songs, suggesting it might be a name. I wondered if it was a reference to one of the titular characters from 1970s detective series Starsky & Hutch, in which driving featured heavily. Both characters in the show were shown to own vehicles, but the majority of the driving was done by Starsky in his Ford Gran Torino while his partner Hutch rode 'shotgun' in the passenger seat.
To 'bump' something is slang for removing someone or something from a particular position. My educated guess based on the above reasoning would that 'bumping Hutch' could mean driving without a passenger, or perhaps deliberately excluding your normal driving partner.
I welcome any constructive comments that would help improve this answer, but would expect any outright dismissal of my conclusions to be backed by evidence.