Increasing the resolution of the curve should do it. DefResolU at the top of the Curve and Surface panel - it's 6 as default - try upping it to 12.
Doing that, making 2 models and taking the straights from one and the corners from the other is probably your best bet.
The other option is to subdivide parts of the model you've already made...
Mesh » Edges » Subdivide, Specials » Subdivide/Subdivide Smooth
...but that will increase the poly count in both directions so you'll end up with two strips of road and will have to either go round merging the poly pairs or just live with the track having a slightly higher poly count than it should.
Doing that, making 2 models and taking the straights from one and the corners from the other is probably your best bet.
The other option is to subdivide parts of the model you've already made...
Mesh » Edges » Subdivide, Specials » Subdivide/Subdivide Smooth
...but that will increase the poly count in both directions so you'll end up with two strips of road and will have to either go round merging the poly pairs or just live with the track having a slightly higher poly count than it should.