Is there some kind of Bresenham algorithm or equivalent for scanline rendering a rotated ellipse?
The classic book Computer Graphics: Principles and Practice (second edition) by Foley, van Dam, et al. describes such an algorithm in section 19.2.

The explanation in the book seems to come from an MSc thesis, Raster Algorithms for 2D Primitives by Dilip Da Silva. 

See also these papers:


Curve-drawing algorithms for raster displays by Van Aken and Novak (ACM TOG, 1985). 
A tracking algorithm for implicitly defined curves by Chandler (IEEE Computer Graphics and Applications, 1988).