Sorry so late. I haven't checked in in a few days.
He has the right away when turning left just like any other driver. It could be state differences in bicycle rules, very possibly.
In Maryland, bikes follow driving laws and are treated like any other vehicle. You can actually get pulled over for a DUI when biking.
My point was that traffic following the bike while making a left turn is often very impatient because they have to follow a slower vehicle. They will sometimes try to drive around the bike which is dangerous and sometimes get angry and throw things at the biker.
This is assuming the biker legitimately has the right of way and are turning on green or an arrow and are in front of the following vehicle. In this case the biker would have the right of way.
Right turns are not nearly as problematic because the bike can hug the shoulder. Crossing intersections seems to really raise the ire of other drivers.
Again, state laws vary and maybe I wasn't so clear in my original comment.