It's not a bad thing that the baby won’t take a bottle. If the baby is getting several bottles at this age, it is quite conceivable that she will reject the breast sooner or later. Babies even younger than yours can learn to drink from a cup. (See the video clip of a baby of three weeks of age cup feeding at our website NBCI.CA.) It takes practice and patience and not all caretakers are willing to do it, but it certainly is not complicated.
If you must use a bottle, then plan to get the baby off it as soon as possible. Just because a baby doesn't cup-feed well at three weeks of age doesn't mean she won’t do it well when she’s four months or six months. If her caretaker cannot manage it, then a better idea would be to start the baby on solids sometime after four months. Better solids taken off a spoon than bottles that really do risk the baby refusing to take the breast. Breastfeeding (as opposed to breast milk feeding from a bottle, cup, syringe or whatever) is about so much more than the milk.
Plus, your milk can be mixed with the solids if you wish. The baby doesn't have to drink the milk. (See Starting solids at the website NBCI.CA.)
I think, at some point, U.S. moms should start lobbying government for decent maternity leave. Anything less than six months is not decent. Anything less than one year is inadequate. In some countries maternity leave is even longer than a year (Sweden, Norway, Slovakia and several others).