The Collaborative International Dictionary of English v.0.48:

Bemire \Be*mire"\, v. t. [imp. & p. p. Bemired; p. pr. & vb.
   n. Bemiring.]
   To drag through, encumber with, or fix in, the mire; to soil
   by passing through mud or dirt.
   [1913 Webster]

         Bemired and benighted in the dog.        --Burke.
   [1913 Webster]

WordNet (r) 3.0 (2006):

bemire
    v 1: make soiled, filthy, or dirty; "don't soil your clothes
         when you play outside!" [syn: dirty, soil, begrime,
         grime, colly, bemire] [ant: clean, make clean]

Moby Thesaurus II by Grady Ward, 1.0:

19 Moby Thesaurus words for "bemire":
   begrime, bemud, besmoke, bog, bog down, dirt, dirty, dirty up,
   dust, grime, mire, muck, muck up, muddy, sink in, slime, smoke,
   soot, stodge