The Puget Sound which includes Bellevue has a decent bus transportation network if you're staying in the city.
Metro (http://transit.metrokc.gov/) offers both local bus service good for short distances and express bus service good for longer distances.
Sound Transit (http://www.soundtransit.org/) offers express bus service.
The two systems accept transfers from each other, treating foreign transfers as credit for a one-zone trip.
For trips outside of the core city, you'll probably want a car.
