I don't know mama, at that age they still need brestmilk at four hour intervals, at least. I think you still need to work on getting ~4oz of milk into her at each of those feeding times. Is it possible she's refusing the bottle at those mid-morning intervals because not enough time has passed between the big nursing sessions. Maybe she's super full from the 7:45 nursing session to take anything at 10:45 (though that seems like plenty of time)? Have you tried other bottles? Some babies are pickier about bottles than others. We bottlefeed and love the Dr. Brown's narrow neck bottles and we initially used them on the recommendation of some local LC's, so maybe give them a shot. You could definitely give sippies a shot, but again, you might have to try a lot of them to get what works. My Daniel is 8 months this week and we've been through about 4 sippies and he JUST started taking one with water at meals. At 5.5 months, he had no interest in sippies but could drink out of an open cup sip by sip.
You might want to start solids just to get a little more food in ADDITION to the feeding you're already giving her, because even the amount you're giving doesn't seem like a ton of food for a 5.5m baby. I know my son (who is FF at that) can't usually go more than 4 hours without getting cranky and hungry. So maybe try some high density foods like avocado or egg yolk or meats.
My youngest sister refused to eat during the day and would only take breastmilk from the breast. She nursed a lot in the afternoons and evenings when my step-mom got home from work. She gained and grew fine. Now she is an adult. My dad said that she did not take a bottle often, but if she got hungry enough she would (he sometimes took care of her during the day).
I think that if your DD is gaining weight and is generally healthy to assume that she will eat when she needs to. Also, my own DD never took a bottle (I was fortunate to be a SAHM with her), but when she started eating solid foods around 6 months she was very willing to eat with whomever was feeding her. She would become irrate if anyone tried to give her breastmilk in either a bottle or sippy.
I don't know if that helps, but that has been my experience.
Partner (10 years) Mother to Lily (4 years), Jonas (1.5 years), 1 dog , and 1 cat