The Collaborative International Dictionary of English v.0.48:

Bespit \Be*spit\ (b[-e]*sp[i^]t"), v. t. [imp. Bespit; p. p.
   Bespit, Bespitten (-t'n); p. pr. & vb. n. Bespitting.]
   To daub or soil with spittle. --Johnson.
   [1913 Webster]