What rueger said.
I've been there before as a new board member of a non-profit, and rueger is completely correct that it takes at least a year to understand how an organization works and why things are the way they are. More importantly in your case, it takes that long to suss out the nature of the personalities involved, and know what is important or not to each director so that you know how best to advance your goals and make it a positive thing for everyone involved, but most importantly the organization itself.
More than any of that though, you really need to study what the appropriate and necessary roles of a director are. Start Googling and reading on the subject -- there's lots of good stuff out there. As a director you are entrusted with serious legal responsibility for governance and oversight of the organization and accomplishing its stated mission. Everything you do must serve those ends and must be evaluated in light of them. This is your primary role and duty -- everything else is secondary.
Your legal duty and responsibility is to the organization. Not to the board. Certainly not to Bob. So first you need to identify how the current situation is holding back the board from any or all of its responsibilities for governance, oversight, or accomplishing the organization's mission. Once you understand that you can use it as a basis of a discussion with the board so that the board can decide whether they want to solve the problem. If they decide as an entire board through an adopted motion that they want to solve the problem, then you can work with the stakeholders such as Bob to figure out the "how" part of solving the problem (unless Bob already agrees that it needs fixing, in which case the two of you may be able to work together to approach the board together with a presentation of the problem and a proposed solution). See how that works? Identify the core duty/responsibility, address the problem in achieving that duty/responsibility, determine a course of action through the board's official decisions, then implement that decision while maneuvering in the zone of the personalities involved.
How does this then apply to your situation? In order for the board to perform its oversight and governance functions, as well as preserve business continuity in achieving it's mission, it is important that they have reliable access to all documents which they need. The degree to which it is easy to locate those documents impacts how effective the board members can be at carrying out those duties. And for the important documents reuger mentioned (minutes, budgets, etc), it is extremely critical to have a solid paper trail, particularly if for some reason your secretary of state, the IRS, or J. Random Attorney With Aggrieved Client comes knocking. Maintaining these records is part of your legal "duty of care", and you need to make sure it is done, and done wetech.slashdot.orgt SuperBanana mentioned further above: Once you've identified the weakness that your board is responsible for fixing, operate within the correct procedures of the board to address the issue. Get the item on the agenda. Let Bob present on how he would like to fix it, or have the board discuss how they would like it fixed. As part of this the board should create and vote on motions that direct the next steps that should be taken (e.g. further research, funding for implementing a solution, etc). At this point it doesn't matter any longer if Bob is on board with the approved motions or not -- though hopefully he is and a plan that he's happy with has been adopted. In any case at this point the board's decision is as good as law for the organization: if any director cannot faithfully support and help execute the adopted motion, whether or not they were in favor of the motion in the first place, that director needs to resign. If the director works to undermine the board's decision and doesn't resign, the board needs to remove them post-haste.
This doesn't have to be as heartless in practice as it sounds in words, but always remember that your first responsibility is to the governance and oversight of the organization, and toward achieving its mission. Use that principle as your guidepost and the rest will come into focus for any and all issues you deal with as a director.