I looked into your question a bit and it seems that not much is known about Shakespeare's work habits.

It does not seem likely, however, that he did most of his work sitting in the sun or lounging in the bathtub.  Shakespeare was probably too busy for that.  He was an actor in a play troupe, so he was busy rehearsing and performing.

It's more likely that Shakespeare did much of his work  backstage at the theatre, and at taverns and inns.  If we could find some of his original manuscripts, I wouldn't be surprised if they had some gravy and ale stains on them. 

(London, where he did much of his work, doesn't have so many great sunny days, and the bathtubs available in the 16th century probably weren't worth lounging around in.)  (: