The sound of Big Ben over the radio was traditionally rendered "Bong" (and sometimes referred to as the bongs, though I wouldn't recommend that in a normal context).
Church bells are supposed to go "Ding-dong" when rung, e.g., for a wedding. I have seen the sound of a full peal rendered "Tin-tan-din-dan-bim-bam-bom-bo" (Dorothy Sayers, if I remember correctly), but, again, would hesitate to use that more generally.
The problem is that the sound of a bell is no more specific than the sound of a voice, so just as people may whisper, murmur, exclaim, shout or many other possibilities, bells may tinkle, chime, peal, clamour, clang..., and each would be 'spelt out' differently.