The Collaborative International Dictionary of English v.0.48:

Bespeak \Be*speak"\, v. t. [imp. Bespoke, Bespake (Archaic);
   p. p. Bespoke, Bespoken; p. pr. & vb. n. Bespeaking.]
   [OE. bispeken, AS. besprecan, to speak to, accuse; pref. be-
   + sprecan to speak. See Speak.]
   1. To speak or arrange for beforehand; to order or engage
      against a future time; as, to bespeak goods, a right, or a
      favor.
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            Concluding, naturally, that to gratify his avarice
            was to bespeak his favor.             --Sir W.
                                                  Scott.
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   2. To show beforehand; to foretell; to indicate.
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            [They] bespoke dangers . . . in order to scare the
            allies.                               --Swift.
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   3. To betoken; to show; to indicate by external marks or
      appearances.
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            When the abbot of St. Martin was born, he had so
            little the figure of a man that it bespoke him
            rather a monster.                     --Locke.
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   4. To speak to; to address. [Poetic]
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            He thus the queen bespoke.            --Dryden.
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The Collaborative International Dictionary of English v.0.48:

Bespeak \Be*speak"\, v. i.
   To speak. [Obs.] --Milton.
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The Collaborative International Dictionary of English v.0.48:

Bespeak \Be*speak"\, n.
   A bespeaking. Among actors, a benefit (when a particular play
   is bespoken.) "The night of her bespeak." --Dickens.
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WordNet (r) 3.0 (2006):

bespeak
    v 1: be a signal for or a symptom of; "These symptoms indicate a
         serious illness"; "Her behavior points to a severe
         neurosis"; "The economic indicators signal that the euro is
         undervalued" [syn: bespeak, betoken, indicate,
         point, signal]
    2: express the need or desire for; ask for; "She requested an
       extra bed in her room"; "She called for room service" [syn:
       request, bespeak, call for, quest]

Moby Thesaurus II by Grady Ward, 1.0:

113 Moby Thesaurus words for "bespeak":
   accost, address, announce, apostrophize, appeal to, apply for,
   apply to, approach, approve, argue, ask, ask for, attest,
   be construed as, be indicative of, be significant of,
   be symptomatic of, beg leave, betoken, book, breathe, brief,
   buttonhole, call for, call to, characterize, connote, crave,
   demand, demonstrate, denominate, denote, desire, differentiate,
   disclose, display, employ, engage, entail, evidence, evince,
   exhibit, express, file for, furnish evidence, give evidence,
   give indication of, give token, go to show, greet, hail, halloo,
   highlight, hint, hire, identify, illustrate, imply, import, indent,
   indicate, invoke, involve, make a request, make a requisition,
   make application, manifest, mark, mean, memorialize, note, order,
   point to, preengage, put in for, recruit, refer to, request,
   requisition, reserve, retain, reveal, salute, set forth, show,
   show signs of, sign on, sign up, sign up for, signalize, signify,
   solicit, speak, speak fair, speak for itself, speak to,
   speak volumes, spell, stand for, suggest, symbolize, symptomatize,
   symptomize, take aside, take into employment, take on, talk to,
   tell, tend to show, testify, whistle for, wish, witness