Bishops weed is very difficult to get rid of. Weed Impede is not labeled to get rid of Bishops Weed specifically, so we are not sure if it will work or not. From everything we have read online, it is very difficult to eradicate.
We did find this online: The only way to get rid of Bishops Weed is with a lot of patience and time on your knees weeding it out of your garden. Bishops Weed likes to grow in the top 4 inches of soil, so don't dig too deep when getting it out. You are bound to miss a few rootlets which will start sprouting again. Just dig them out as they show up, and be persistent! Edging can be useful as you weed the garden area, as it will allow you to work smaller areas at a time without worrying about re-infestation from surrounding areas (weeds love that nice fluffy soil) You can try a heavy dose of Round-Up in early fall before the weed goes into its winter dormancy.
Unfortunately Bermuda grass is so closely related to St. Augustine grass that there is nothing that will remove Bermuda from St. Augustine and not hurt the St. Augustine as well. In your situation it is recommended to spot treat the Bermuda with Round Up and kill it directly, and then replant St. Augustine in those areas. We do carry some professional round up products: http://www.domyownpestcontrol.com/nonselective-herbicides-c-188_408.html
Monterey Weed Impede 2 in 1 Herbicide contains a combination of Glyphosate (a non selective herbicide) which will kill anything that it is sprayed on, and Prodiamine which is effective in controlling weeds even before they emerge. It could be used on dormant lawns for preventing the listed weeds on the product label. If your lawn is currently growing and greening up it would not be recommended to be used as it can kill it as well. Prodiamine 65 WDG is a stand alone pre-emergent that could be used. To kill existing weeds, we would need to know the type of weeds you are trying to control, grassy or broadleaf, as well as the type of grass your lawn is.