In principle this should work:
pts = {{-1, 0}, {-1, 1}, {0, 0}, {1, 1}, {1, 0}};
g = Graphics[{FilledCurve@BSplineCurve[pts, SplineClosed -> True]}]
DiscretizeGraphics[g]
But as you can see, the result is wrong.
This may be the same bug as described here:
You may want to report it to Wolfram again in the hope that more reports equal a higher likelihood of fixing it ...
