Many rentals in Bend accept pets since it's a very dog-friendly town! You can start with checking for properties on Craigslist or contact individual property management companies. The rental market is very tight and the better rentals go fast so you need to be ready to commit quickly. Unlike in other states, real estate brokers do not handle or have access to rental listings. Erika Morris at Morris Hayden Property Management handles all of my clients' investment properties and usually has a good variety of available homes to choose from. You can find them online at http://www.rentbendoregon.com.
Plus Property Management also tends to have a good selection of properties, http://www.investoregon.com,
as does Bend Property Management. Unfortunately, since brokers can not show you multiple rental listings by various companies you will need to contact each company separately if they each have properties of interest to you. I work with many relocation clients so I know how challenging it can be to find a nice rental! Good luck!
David D. Gilmore
Coldwell Banker Morris Real Estate