In my experience wood ash dumped on an already alkaline asparagus bed does not affect production. I dumped a lot more than you, too, and certainly the mineral content of that bed is going to be good for a long time. Other plants may not be so tolerant of alkali on top of alkali, but there was a reason why NASA announced that you could grow asparagus on Mars (you may not be able to grown anything else in 8.3 soil).

OK Glib. No asparagus on Mars! LOL
I'll just let the rain this weekend do it's thing.
I usually take the ashes out to a far corner of our acre to the "out there" compost where I take the too large tree branches, weeds that are flowering and other stuff that won't break down fairly quickly in my compost piles. Nancy

You've inspired me. I think I'll dump the next load of wood furnace ashes on the asparagus bed :)