The Collaborative International Dictionary of English v.0.48:

Blas'e \Bla*s['e]"\ (bl[.a]*z[asl]"), a. [F., p. p. of blaser.]
   1. Having the sensibilities deadened by excess or frequency
      of enjoyment; sated or surfeited with pleasure;
      uninterested because of frequent exposure or indulgence;
      used up.

   Syn: bored.
        [1913 Webster + WordNet 1.5]

   2. very sophisticated; versed in the ways of the world. the
      blase traveler refers to the ocean he has crossed as `the
      pond'

   Syn: knowing, worldly.
        [WordNet 1.5]

   3. uninterested and attaching little importance; -- of
      attitudes toward duties. a blase attitude about
      housecleaning

   Syn: unconcerned.
        [WordNet 1.5]

Moby Thesaurus II by Grady Ward, 1.0:

157 Moby Thesaurus words for "blase":
   Laodicean, Olympian, aloof, apathetic, ataractic, benumbed, blah,
   bored, carefree, careless, casual, comatose, cool, cosmopolitan,
   cosmopolite, dead, debilitated, degage, desensitized, detached,
   devil-may-care, disabused, disappointed, disenchanted,
   disillusioned, disinterested, dispassionate, dispirited,
   disregardful, dopey, dormant, droopy, drugged, dull, easy,
   easygoing, emotionless, enervated, enlightened, exanimate,
   experienced, fed-up, free and easy, good and tired, heartless,
   heavy, hebetudinous, heedless, hopeless, in a stupor, inanimate,
   inattentive, incurious, indifferent, inert, inexcitable,
   insouciant, irked, jaded, knowing, lackadaisical, languid,
   languorous, leaden, lethargic, life-weary, lifeless, light-hearted,
   listless, lumpish, mature, matured, melancholic, melancholy,
   mindless, mondaine, moribund, negligent, nonchalant,
   not born yesterday, numb, numbed, offhand, old, passive,
   perfunctory, phlegmatic, pluckless, pococurante, pooped, practiced,
   put straight, reckless, regardless, resigned, ripe, ripened,
   robbed of illusion, sagacious, sated, satiated, seasoned,
   set right, sick, sick of, slack, sleepy, slow, sluggish, somnolent,
   sophisticate, sophisticated, soporific, spiritless, splenetic,
   spunkless, stagnant, stagnating, stoic, stultified, stupefied,
   supercilious, superior, supine, tired, tired of, tired of living,
   tired to death, torpid, tried, tried and true, turned-off,
   unanxious, uncaring, uncharmed, unconcerned, undeceived,
   undiscriminating, unimpressed, uninterested, unmindful, unmoved,
   unsolicitous, unspelled, vegetable, vegetative, veteran, wan,
   wearied, weariful, weary, weary unto death, withdrawn, world-weary,
   world-wise, worldly, worldly-wise