asparagus v bindweed

Despite my careful clearing before I planted my asparagus, I have the same bindweed problem. When the bindweed shows it's face, I pull off most of the growth leaving a short stub above the ground and immediately give that a spritz with glyphosphate (on a non-windy day). It's the only way to restrict it's growth among asparagus roots. I find that an early season spraying sets the bindweed back for at least 2 years or more. You just have to keep watching for fresh growth in other areas and do the same as there's never just one or two clumps of the stuff.
If you feel nervous about spraying, hold a piece of newspaper or cardboard behind and around the bindweed stump so the spray can't spread.

Another way of doing it would be when a bindweed shoot shows, plant a milk carton around it with the bottom cut off, and a bamboo cane, and leave it a few days and wait for the bindweed to start climbing the cane. Once it reaches a decent length remove the cane and unwind the tendril, and curl it into the bottom of the milk carton - then you have a decent amount to blitz with spray, in a confined area.