Possibly I have misunderstood what the phrase "riser bars" means, but otherwise, IMHO, bullhorns have as many hand positions as do riser bars, if not more.

That said, I ride with bullhorns and, since my bike fits me perfectly, I keep my hands in the same position all the time without any discomfort.

It takes a long time and considerable thought and reflection to find the right fit.

It took me three years and a lot of experimentation to get my present bike "just right."

It helps to have either too much money or an LBS who will let you experiment out a parts box.