I'm chairing a bylaws committee in my organization this fall. I searched for months for information on how to run a bylaws committee, both advisory information and requirements of Robert's Rules, and concluded that there were few strict requirements for how the committee works. The only requirement, the way I interpret things, is that the bylaws committee must eventually adopt a single complete document as its report, which would be the revised bylaws if the will of the committee is to produce a complete revision.
I'm not an experienced parliamentarian (or even an RP), but I'll share how I've been running the committee I chair: We've had several meetings focused on particular topics—for instance, rules for officer elections, membership provisions, and powers of the executive board. These have been informal discussions, and most decisions have been reached by consensus, though I've called a couple of votes on subjects where divisions were intractable. At these meetings, I've focused on practical issues, ranging from broad to minute matters, but omitting anything that I think is simply a technical matter of how to turn a well-defined idea into bylaws language—and the committee has been happy to grant me that discretion at least for now.
In parallel, I've been creating a working draft of the proposed revision, which any member can access and comment on—though I am the only person who can actually edit the draft (since I want to avoid the problem of too many cooks stirring the pot, which is the reason why our current bylaws are such a mess in the first place). I've been updating it in accordance with the consensus reached by the committee, filling in gaps according to my judgment of what best reflects the committee's will. After we finish the subject-matter meetings, I'll finish the first draft, then bring it to the committee for an informal discussion. If changes are suggested, I'll incorporate them into the second draft, which I will bring to the next committee meeting for a formal vote after possible amendments. Once we vote to report the revision, I'll give notice to the full membership at a general meeting (as our current bylaws require) and move adoption at the following meeting.
This is an organization that meets frequently, but is generally uninterested in parliamentary and organizational matters—though my committee has benefited from a variety of active contributors from various factions of the organization. You'll have to run your committee a little differently depending on the structure and dynamics of your organization. I don't claim that my method is perfect, or even good—it's just how I've been doing things, both in terms of my plans and the direction the committee has chosen for itself.