The character limit is always an issue. It forces us to be creative. XD
In the past I've done everything from the text of a simple, white business card that listed only the character's name, his position and the company he worked for to short diary fragments (The Nemissary's bio was an entry from The Unquiet Bride's diary, while hers was a selection from his-). One character had the Poem of Life. Another (a golden lady robot named Metropolitan-) had a bit of dialogue from 'Metropolis'. Another (a Time/Archery guy named Arjuna) had a passage from the Mahabharata.
For most I just go for a short bit of in-character dialogue, though. I find that to be a word-count-friendly way to give a solid, general impression of the character as an individual. If space allows, I might also add a separate [RP NOTE] entry at the bottom, or a bit of OOC text about who and what the character is, but I don't always have that luxury.
I'm still working on my current Homecoming characters', but here's one of those "Conversation bios" from one of my original Liberty mains as an example. This one belonged to Grey Kestrel, my Rogue Stalker who, even after the railroad-a-rific mess of the Patron arcs, remained exceptionally devoted to Scir. (The 'Cardinal' she mentions was her perma-summoned Adept partner, who was basically roleplayed as a whole separate character unto himself-)
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"Listen, hero... You don't know us. You don't know jack about who we are, or why we're here. You just see some Arachnos assassin and one of those damned Mu mystics out to spoil your fun, don't you? 'Here to rain on your sunny little parade. Well, it's time to catch a clue, cape... It's not like that.
"We aren't your enemies, and this has got nothing to do with Recluse. We're not doing this for him. So get your hands off of Cardinal, and stop trying so hard to make me kill you."
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That pretty much sets the whole tone of Kes as a person, even if doesn't give away a huge amount of specific information.