I grow both but
side by side, they would not do well in in the same bed.
In spring, as the asparagus spears are about to emerge, the saffron leaves are in full foliage. The saffron would shade the asparagus and they would compete for nutrients.
Harvesting the asparagus would be difficult amongst the foliage.
Both are heavy feeders.
Saffron corns multiply rapidly grown in ideal sonditions. Each corm is able to produce up to six daughters that form below the mother, pushing the corms up through the soil. Even with regular thick mulching, the saffron needs to be dug up and thinned every four or five years for optimum flower production.
We grow for domestic use and harvest enough to cook with ourselves and give to friends.
Asparagus is shallow rooted and does not like being disturbed.
My strong recommendation is to keep them separate.