I haven't been there for years, but used it a fair bit when I lived in Leicester. I would say it is quick drying and can't remember ever going there and not being able to climb. I left Leicester in 1984 so memories may have faded, but I remember there were some good pubs nearby!
Probably not the most useful reply, but since no one else has replied maybe better than nothing.
...pretty quickly especially if there's a bit of wind. Some areas seep a bit but you can just pick and choose. Looking at the forecast I'd say it will be damp-ish Thursday night but pretty good Friday.
I just remembered something else. On top of the bridge there is a course of heavy coping stones. Some of them have slots in that you can get your fingers in to use as you top out. We were always worried about how well fixed they were and maybe they could pull out. They must have weighed at least 50kg so if one of those landed on you, game over.
You may wish to know that sometimes the nettles grow up a fair bit on either side of the bridge buttresses,(though different climbers do cut them back at times with lawn mower or strimmer) so not always the best idea to turn up in shorts: But then it is not the warmest May that we have had.