First find out what kind of grass you are dealing with. You can take it to a garden center not a box store like Lowes or Home Depot and they may be able to tell you. Knowing what you are dealing with will help. You would treat Johnson grass different than you would rye grass. Some grasses if you leave a smigin of root a new plant will form. Some you can leave everything other than the crown and problem solved.

The single best means of keeping grass from invading a planting bed is a barrier of some kind and which barrier is determined by which grass is doing the invading. If the grass roots near the surface and also spreads by stolens (near the soil runners) the relatively inexpensive plastic 4 or 6 inch edging sold in most any garden shop will work. But if what you have is quackgrass or Johnston Grass, with rhizomes that search out new territory deep down, you will need something that will block them at that level and for that I use 10" aluminum flashing, although some others have used that plastic carpet runner cut in half.
Temporary measures involve spraying poisons to slow down the invasion.

I do have concrete curbing dividing this bed from my lawn. But the grass in the flower bed is not the same as my lawn.

I realize concrete curbing is wholly inadequate for preventing the spread of grass. But as I said, this grass doesn't appear to be coming from my lawn. The blades are completely different.

My lawn is pretty healthy - there are a few spots of Johnson grass here and there. But they aren't prevalent.

I'll have to see if I can ID the grass I'm dealing with.

Is it grass or one of the nutsedges?

My Mom has a huge Johnson Grass issue. She used Ortho Grass B Gone on part of the bed and left the remainder untreated as an experiment. The areas where she used the Grass B Gone are nearly devoid of the stuff whereas the untreated areas are more thickly infested than ever. Her perennials seem to be uneffected.