First of all, be sure your activity profiles are the same for the unit and Basecamp, shortest or fastest. Fastest usually means to prefer interstates unless they're excluded and shortest might do something stupid like go across Atlanta on surface streets. But if you have shortest selected in Basecamp and the GPS is set to fastest it'll often insist on taking you to the interstate at every opportunity.
Then using Basecamp make multiple waypoints along the route you want including starting and ending. Holding down the control key, click on each waypoint in the lefthand box in order along the route. Then File > New > Route Using Selected Waypoints. That should prevent it from wandering off in various directions.
You can also insert route-shaping points using Tools > Insert. Create a route, then click on the highlighted route near the beginning; you should see a dark line appear and the route should go to that point. Move away from the start (use the arrow keys to scroll the screen) and click another point; the route should extend through that point, etc. You can use lots of shaping points to force both Basecamp and the GPS to follow the planned route.
I've been using shaping points partly to avoid cluttering things up with so many waypoints and also so the GPS doesn't loudly announce that I'm approaching a waypoint.
Basecamp has a rather steep learning curve and it's certainly not intuitive how it and the GPS interface. Help > Garmin Forums and the Yahoo group https://groups.yahoo.com/neo/groups/Garmin760/info are useful.