Is it a good item choice for ashe? the mana regen + dmg increase seems like a nice idea.

Probably not. Ashe does not have mana issues except for her laning phase, and she can benefit much more from an early Banshee's / Brutalizer / Inf. Edge.

crit damage/AD seems a better choice

who would be a better champ using the manamune?

Ezreal works well. Basically, if you already get +mana items on the champ, and physical damage is important, then you should consider it. IE Ezreal standard build includes sheen so that synergizes with manamune to some extent.

Other champions who could benefit include Nasus (only in an offtank role or pure dps [which is bad]). I've seen Miss Fortune players get it although I don't play her so I don't know. Sivir can also use it, in which case you should get probably a Bveil (which gives you 2 spellbreaks every 30 sec if you want) instead of standard chalice. Kayle maybe, although other items are more important for her. Other than that I don't know.

Manamune is pretty epic on Eve (yeah, Eve.) because spamming hatespike gets your mana (and thus AD) up really quickly. With the AS from her ultimate you can deal some serious damage.

I don't think manamune belongs on Ashe, Ezreal, or Miss Fortune. Mana regen glyphs/seals + 21 util (if really needed) cover mana problems for them, so manamune is just an overpriced BF sword that doesn't build into anything.

But...doing the math, if you have one or more item in your build that has + mana, it becomes more cost-efficient than BF swords.

For example, Nasus. A standard build might include a Sheen and a Banshee's veil already. I don't have the stats in front of me but I think that is 750 mana total. Add in the + mana from manamune's passive, and unique, and you would end up with + ~2000 mana. Add in the character's inherent mana and you have a beastly 90+additional damage from one item.

For Ez, you build a sheen, or you're bad. Add in Manamune and that is still a bonus 80 damage from a 1900 cost item...plus you can put your blue runes into CDR or MR or something else useful!

Its epic.