You will not get rid of Mares tail with just digging once. Sadly it is a very persistent problem. You would need to damage the leaves and then spray with Round up or any other weed killer which is absorbed into the plant. You will need to do that for a fair number of times to be sure of getting rid of the problem. Sorry.
Using a weed killer like Sodium chlorate (probably banned now( will leave the soil unusable for 6 months.

I think you are going to need to find somewhere else to plant your spring flowering bulbs as Owdb. has already stated getting rid of mares tail requires a lot of effort.

You could clear as much as you can and then plant your bulbs in special bulb baskets that are designed to be lifted out after flowering, and then you could continue the battle. The grass battle is more or less winnable by dedicated digging out, but the horsetail (mare's tail is the aquatic version) is a much tougher challenge as the roots can be extremely deep (six feet or more)and you could consider using containers a for a few years until you have won as they can be moved to one side while you treat the horsetail again (and again...)
Be watchful in spring -the first horsetail shoots are different - just a spike with knob on top. These are the fertile heads and should be removed before the spores ripen and disperse. Membrane isn't a solution as they can sometimes penetrate even that.