To add detail,

This has progressed over the past few years to just a little to overtaking the flowerbed.  I have checked with local gardening stores and keep getting the advice to pull it out.  I think that makes it worse as I can't get all of the roots so I think it springs up more sprouts each time I pull it.  I do not want to use a herbicide such as roundup.  It is in the ground around flowers such as daylilies where I can get to it but also in the middle of decorative ivy that I can't separate it from the out wanted plants as well.  

Your id is correct. This is an aggressive weed and difficult to control. If you desire not to use chemical control, you will have to pull every 3 weeks or so, to wear down the energy of the weed. This will take quite a bit of time. Like years. If any root is left over 2 inches, it can reproduce. If using glysophate, (Round Up type product) spray when the weed is blooming and begin a schedule of sprays. Here is an article with some good information: https://www.oregonlive.com/kympokorny/2008/09/bindweed.html
This factsheet will list ways to irradiate in different areas of your lawn. http://ipm.ucanr.edu/PMG/PESTNOTES/pn7462.html