For the title question, our existing Q&A How should I phrase an important question that I need to ask a professor? applies - professors are human people that communicate with other human people using words, but they're often busy so it's best to phrase things concisely and directly.
However, do consider that you've made a commitment to do research with B, and especially as someone learning to do research (that's the whole point of a PhD), you should expect your research to be a full-time job.
If you have a proposed project with B scoped to be a reasonable basis for a PhD degree, and a proposed project with A scoped to be a reasonable basis for a PhD degree, that's two full-time jobs. You say you don't think it would be difficult, but... if it wasn't difficult enough to be a substantial time investment, it's probably not very interesting research. I'm guessing your estimate of the time involved is a bit off - it's even difficult for experienced researchers to estimate time required for a given project (except with more experience you learn to multiply your initial estimate a few-fold)!
I'd recommend if you do reach out to A, you keep commitments vague (for example, expressing hope and interest to do the proposed work "some time") and get settled in to your primary research project first. Then, if you're actually feeling like you have a bunch of free time to commit to the project (I'm skeptical, but you might prove me wrong!), suggest it to your PhD advisor B as a side-project to improve your breadth of experience before committing to the project and setting a definitive plan with A. I wouldn't recommend taking on a substantial side-project without your primary advisor's approval.