unwanted u turn

Which device?  Why is it unwanted?  Are you sure if using an automobile device you don't have a waypoint the wrong side of a divided highway?

It's in a route I created in Basecamp after moving a portion of the original route to a route using an alternate road, a 2 lane undivided highway.  I simply want to continue along the selected road but Basecamp has me making two U turns going back about a mile then reversing course and then continuing in the desired direction.

OK I fixed it by deleting one of two "shaping Points" near each other and that has eliminated the problem. The person who suggested somewhere that Basecamp has a steep learning curve was indeed correct!

Nope, but you put the point on the wrong side of a divided highway.  To reach that point and continue your route you had to make 2 u turns.  If you hadn't been routed that way and did actually want to visit that point you'd be asking why BaseCamp had skipped a point ;)

Absolutely not a divided highway, a two lane county road,

Then perhaps something else was wrong with those shaping points requiring a u turn, are you able to post a link to the gpx file?

This will happen if you place via or shaping points out of order.  So the route was directing you to the further point first, then directing you to turn around and go back to the closer point.