consider just teaching her to drink out of a cup (that a parent holds and tips and etc.)
premies can't suck and drink out of special flexible cups ... hearing this made me question the entire bottle/sippycup thing ...
anyhow, one grandma used sippy cups (because she let them wander around the house with juice etc.) but none of the rest of us used them, on my kids ...
I *do* recommend the shape of cup that Tupperware makes ... I am not up on all the plastic/PCB stuff lately (I just told one friend, I'm gonna keep using my stuff, because I'm sure it's old enough that we've already leached out all the bad chemicals so it's not gonna hurt us now ;) sigh! ) ... so I don't know if Tupperware is now verboten ... but the flared-out shape is easier (by observation, not according to any doctors or anything) to Not Spill While Drinking.
And at 5.5 months, it's not the greatest, but she can go a whole workday without breastmilk probably, as long as you nurse before you leave and when you get home. Pureed babyfoods or whatnot will keep her tummy full. Getting her to sleep when she's tired without nursing will probably be the biggest problem!