Scott,
I have seen various models for building the operational TBM office. The main factors that determine the size and shape of the TBMO have been: 1) Who is maintaining the tool (Finance or IT) 2) Users of the system - is the tool just for IT and Finance or has it been rolled out to the business 3) How many Apptio solutions do you have running ( Cost Transparency, IT Planning, Bill of IT) and finally 4) Is your organization support model centralized or de-centralized?
One common component to all TBMO is the governance process. All TBMO I have worked with create some type of governance model to ensure the solution has proper change and configuration management. I have seen this function be a single person or part of person as it depends on how large is your Apptio deployment.
The number of TBMAs you have has also ranged from 0 (completely outsourced TBMA function) to 7 for very large Apptio deployment supporting data loading, report writing, model changes and support for over 3,000 users. Typically there are between 1-2 TBMA for an organization that is running one fully operational process (Costing, planning, invoicing) across the business. That scales to 3-5 for customers running multiple processes/solutions. I have seen successful models that have a dedicated TBMA per solution and a TBMA that supports multiple solutions. The complexity of your model and solution will drive the number of TBMA you need.
Hope this was helpful
-Pete