Bither rhymes with:
atither, dither, hither, ryther, slither, smither, whither, wither, zither, altogether, another, atither, bather, bellwether, birdfeather, blather, bother, breather, brother, cather, crowther, dither, either, fairbrother, fairweather, farther, father, feather, forefather, further, futher, gather, genther, get-together, ginther, godfather, godmother, grandfather, grandmother, grether, guinther, heather, hesther, hither, huether, koether, kuether, lather, lawther, leather, lowther, mather, mayweather, meriweather, meriwether, merriweather, merriwether, mother, neither, nether, norther, nother, oldfather, other, prather, raether, rather, reither, reuther, roether, ryther, sather, seither, sether, slather, slither, smather, smither, smoother, smother, souther, starkweather, stepfather, stepmother, stikeleather, strother, suther, tether, together, weather, werther, whether, whither, wither, wrather, yother, zither
Bither sounds like:
bader, badour, badura, bather, bator, batra, batter, batterer, battery, bauder, bavadra, baytree, beater, beaudreau, beaudry, bedore, beefeater, beiter, betar, betray, better, bettor, bidder, bitar, biter, bitter, boeder, botero, bother, bottari, boudoir, boudreau, bowater, boyter, buddier, buder, budreau, budrow, bueter, butare, butera, butter, buttery, buttrey, buttry, bywater