How thick is the mulch you put down?
That "grass" looks very much like a sedge, a grass that grows most often in moist soils, and the seeds may have been in the mulch.

Thanks so much for your answer. The mulch is probably a couple of inches thick. The grass/weed is growing, as you can see in the photo, in the soil surrounding the edge of the bed where there is no mulch. It is really heavy in areas of mulch and of soil. The soil around the edge of the bed is regular yard soil that was tilled when making a spot for the bed, and it's even growing there. It is almost like these seeds were airborne. I looked up some of the different sedges, and I don't think it looks like this grass/weed as it grows. Any other suggestions as to what this might be???

Don't know what the weeds are. The tilling may have encouraged some pre-existing weed seed to germinate. For areas you don't intend to plant in, newspaper under the mulch helps but nothing is perfect.

With a mulch thickness of a "couple" of inches, just barely enough, many "weeds" can still get enough light to germinate and grow, so if only a "couple" of inches of mulch can be put down (cost, asthetics) that should be on top of newspaper, although that "couple" of inches of mulch will allow the newspaper to be seen on close examination.
If not a sedge and if not from the grass along the edge rooting in under that mulch, you have some other grass type of "weed" I'm not familiar with.