Who's In Control?

See this weed. It is one of two main menaces in my flowerbeds. It is a vine never quits growing.

The stems and leaves are covered with tiny hairs that cling to everything; my clothes, my flowers, my cats, everything. All summer long I find them wound around my flowers, choking the life out of them, which infuriates me. Diligently I try to track them down to their roots and pull them at their source, but they have so many underground runners that I have little hope of ever getting rid of them. Yesterday, I tried to rid an area of them as I weeded. It should have been be easy since they are only 6-8 inches tall at this point. However, with all of the bulbs that are sprouting now, I ended up pulling them up as well and spent more time in damage control than in eradicating the menace. Grrrr.