Private buses that do regular routes, such as regular bus lines.

Yes, "buses" at the beginning seems to refer to "transit buses", that is, public transport buses. Here is a reference to toll exemptions on this bridge, from an official document on the project ("SR 520 Bridge Investment Grade Traffic and Revenue Study"):

"Toll exemptions as outlined by the Washington State Transportation Commission (the largest of which is the transit buses, private regular route buses such as the Microsoft Connector, and WSDOT sanctioned vanpools) are assumed."

Transit buses are defined here:
"A transit bus (US), also known as a commuter bus, city bus, or public bus, is a bus used for short-distance public transport purposes. The roles and specifications of transit buses are not clear cut, and vary with operator and region."
http://en.wikipedia.org/wiki/Transit_bus

Transit buses can be operated by public or private agencies/companies; the point is that they are available to all passengers, who pay a fare. However, the example of the Microsoft Connector suggests that "private regular route buses" refers not simply to buses operating regular routes run by private companies (because this could include transit buses, ie., public buses run by private companies), but private company transport covering regular routes. This might regular include services for transporting employees to and from work, such as The Microsoft Connector, or school buses, for example.

"WASHINGTON - It started with five routes and a dozen buses. Nineteen routes and 53 buses later, Microsoft's employee shuttle service has become ubiquitous in neighborhoods around Seattle and the Eastside.
The Microsoft Connector, which began in September 2007, is now one of the largest company-owned employee bus services in the United States, Microsoft says.
The white buses shuttle workers to the Redmond campus from stops in West Seattle, Ballard, Wallingford and other areas where public transit to Redmond is indirect and time-consuming. The buses move employees across the region's clogged roadways in comfort and style, with secure Wi-Fi service, comfy seats, luggage racks, electrical outlets and cup holders."
http://www.mentoreng.com/news-resources/news-listings/micros...

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Note added at 4 hrs (2012-02-10 10:12:06 GMT)
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I forgot to include the URL for my first reference. It is
http://www.wsdot.wa.gov/NR/rdonlyres/A3B026EC-C9AF-4B43-BA31...

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Note added at 4 hrs (2012-02-10 10:13:28 GMT)
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You might say "operating regular routes". There are several ways of expressing it. But the key point is to distinguish between buses run by private companies (which may be available to the public) and private buses, which is what this refers to.

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Note added at 4 hrs (2012-02-10 10:17:54 GMT)
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In short, "private" refers here not to who runs the buses but to who uses them.

As opposed to a public bus that may still run on a regular route but is, of course, not owned by a private company. I think Greyhound might be an example of one in the U.S. (?)