To SH..why is she not ready for finger foods? Try different foods? I NEVER have a daycare child still on anything resembling baby food at pushing a year old. Never in 14 years, nor my own child, who is almost 17. Just keep offering things, eventually she will get it..and once she does, likely it will be a quick escalation to ONLY finger foods!
I have 2 daycare kidlets right now...one just hit the first birthday this past weekend..the other a month ago. I haven't offered baby food or mushy food to them for months. They get mostly what the other kids get..chopped small, made softer (like our grilled cheese today...lightly toasted for them)..along with blueberries and bananas. Mine eat sandwiches and wraps and soups (the drained out chunky parts..perfect for them..soft, etc)...fruits of all sorts (berries and melons right now!) and veggies.
Today we are cold turkey with no bottles. It will be a rougher few days, but they will be fine.
As far as a cup..try other ones...soft nipples, firm ones, ones with or without valves...I would give each one a few days exclusive use (I prefer the no valve ones..less to wash..milk/formula flows right to their mouth without needing to suck it out). More mess, but I get kids off sippys about 18-20 months at my house (and potty train totally at 24-28 months without exception).
Currently I use the Nuby rubbery ones (easy grip no spill cup http://nuby.com/en/nuby/cups-spouts/889) Inexpensive, easy to wash, etc.
Good luck!