The only real way to control invasive grasses such as Bermuda and a plant such as Bindweed is to dig in and remove the roots. Crab grass, an annual, can be easily controlled by recognizing what newly germinated Crab grass looks like and pull those out as they germinate. Very few plant poisons will kill those "weeds" and not the plants they grow with.
Wiping some plant killer on the leaves of each "weed" canbe more tedious then just digging them out.

what kimmsr said.

Removing *any* grass is a pain:

even if you kill it, you still have to dig out the roots, & that disturbs your garden plants.

I probably would dig up the whole bed, set the flowering plants aside, dig out the grass roots (it's easier if you let them dry out & shrink for a few days), & then put the flowers back.

Best luck!

I use Ortho Grass-B-Gone on Bermuda grass when it gets in flower beds. It comes in a 24 oz. spray bottle for six or seven dollars. There are other brands of grass only killer as well. You can spray it on the grass in flower beds it won't hurt the non grass plants in the least. I'd hate to try garden without it because as you know Bermuda grass roots go deep making it hard to pull out. One little sprig left will grow more grass. Be aware that it takes about TWO WEEKS before the grass dies, but die it will - right down to the roots.

I used the active ingredient in Grass-B-Gone this year on my flower beds to go after the quackgrass. It worked really well, killing a lot of it, but otherwise stopped the growth which allowed the flowers to outgrow it. I didn't see any sign of damage to the iris or other flowers, with the possible exception that lilly of the valley may not like it very well. However, my lillies didn't appear phased. I'll have to wait until next year to be sure, but it didn't seem to bother the tulips or daffodils, either.

I've tried other grass killers that also worked well, however they would also hit some of the non-grass flowers, including the iris.

Don't know how this relates to bermuda grass, but at least it does appear to be pretty safe.

If you get rid of the bermuda grass, though, and open up the ground, you'll need to fight more broadleaved weeds also. A shot of Preen early in the spring will really help keep those weed seedlings down.

No herbicides should be sprayed near irises if you want the blooms to look normal in the Spring. Irises are very sensitive to all sorts of herbicides, and the flowers get deformed. I hand pull around the irises then use round-up with a teeny tiny sprayer and a toilet paper tube to direct the spray and keep it from drifting.