Certified GKH Gardening Expert
I usually wait until the leaves at least start to fall over before I cut them back, but it depends upon the kind of bulb. My iris bulbs take a very long time and sometimes never do fall down or turn yellow. A light mulching over your bulbs to protect them from frost shouldn't hurt, but a heavy mulching could hold too much moisture in the soil and cause them to rot. Depending upon the amount of herbicide in your mulch, it shouldn't hurt the bulbs. I hope this helps.
Here's a page that contains articles about lots of different bulb plants and tips for cutting them back: https://www.gardeningknowhow.com/search?q=cut%20back%20bulb%20plants