Any tips on trying to transfer units?

I am currently on a BMM position and would like to transfer to another unit at the end of my BMM time to try and further my career and to deploy this coming year. I am a 91B assigned to an aviation brigade and I am wanting to go to our sustainment brigade. I was told I needed to get a letter of release from my currant units brigade CSM and a letter of acceptance from the sustainment CSM. Is there a way to not offend my chain of command when I talk to them about this just incase they won't sign off, and is there anyway to try and go to a specific company in the sustainment brigade? My neighbor is in the sustainment brigade and told me they had open mtow slots for 91B.

The chain of command for my company has changed out since I've been on BMM also so I'm not sure how my 1SG or commander will react to this request.

Any help on making the process easier, or tips on not burning bridges or offending anyone would be greatly appriciated.