We send a BOV to all our client building owners every year free of charge and we also collect data from local appraisers to build our own comp records. Data

To the degree AVM's aren't reliable, access to MLS data is probably not the issue, though it is a common misunderstanding about AVM's.The real issue with AVM's is that they are based on public records data which doesn't include a lot of important details like floor plan, curb appeal, view, quality of neighbors, etc.

Zillow just collects public records data and makes it available to you.

I have a number of tedious tasks (compiling tax records, data entry, etc.) but I wanted to see how you guys use your VA's.

I pulled public records data on lots in the city that were over 10,000 square feet, then showed them how many were owned by investors.

IMHO decent public records data and transaction history.  

Will the property appraiser during the refinance process appraise the property as a 5/2 bedrooms or will use the public records data 3/2?

If you value your time you'll end up using a 3rd party service that collects, collates, cleans, appends, etc the base public records data into something usable.Ownership and characteristics (beds, baths, etc) are sourced from county assessor offices.

you can probably look the property up on the town property records data base online, let me know if you need help :)

If they do not have online, simply put in a Open Records Data request to the county.