Tear's upgrades are surprisingly good at giving ratio heavy champions a gigantic buff to their late game if you build your items around it properly. UNFORTUNATELY, it drains your mid game strength completely, being a near useless item combat wise as tear and terribly inefficient as, in this case, Manamune when you don't have much mana. Of course it depends on how proficient you are at stacking it - you may stack it to Muramana fast enough to flat out buff Ashe's mid game - but the point is until that thing is stacked, Ashe is especially weak.
Ultimately, Ashe's high base AS makes her a relatively good candidate for Tear. If you have a support (or even entire team comp) dedicated for defensive wave clear and peeling, this can buy Ashe a lot of time to build up her Tear for the Muramana to start tearing through people late game. Essentially, a "Protect the Ashe" comp.