What kind of grass is this
I believe this is quack grass, a perennial creeping grass that can be quite invasive. Hand pulling and digging is minimally effective due to the extensive underground stems (rhizomes) that regenerate new plants after pulling. unfortunately I do not know of any selective herbicides to control it, but nonselective products like Roundup can work, but Roundup can also kill the desirable grasses as well. You can spot spray the unwanted grass and reseed with bluegrass to get desirable grass to establish the area.
Thank you for the question and good luck!