I played my EC mule Dramor quite a bit solo in dungeons up to 52 (KC/CoM, but also SolB). If you think about it a tick, everyone and their brother can solo a fungi monk to 60 and Bards stack up reasonably:
Bards get max defense skill, slow song, and regeneration song which is basically a second fungi. Dramor was still getting pasted at 50 or so, but he was in Lambent not Dwarf armor and IIRC Bard defensive skills also got a boost with Velious. Bards can also fear-kite the last 30% or so and take no damage at all while regenerating. I'd say the Bard is actually ahead of the monk here.
Bard weapon ratios are actually quite good, and they can supplement their damage with song/ss bracer damage shields and chants. If we guesstimate 20 dps melee, 8 dps damage shield, and 15 dps from two chants, that's a solid 45 or so. Way ahead of the soloing Paladin videos, and not all that far behind a Monk.
Monks can FD, but Bards can mez and heal up. I would guess that a Bard could kill anything <=55 with enough patience. I would definitely hesitate to lull rooms of 3-4 on a Bard unless I could zip to the zoneline, though.
And we haven't even talked about Charm; basically everything you said about distance from the mob applies to Bards, and they can even run away while recharming.
The biggest weakness of Bards is that they get zero HP buffs: no shielding, no runes, etc. So you can go down pretty fast. Fortunately there are a lot of epic clerics on P99
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TLDR: Enchanters are better, but Bards can definitely solo in dungeons.