I've found at 4 months was a bit late to introduce bottles so we've went straight to an open top cup. She's been doing very well with it.
Pumping wise I pump first thing , so I feed one side and pump the other, try to get 4 oz or so from that 1 pump , however if I don't I try again 2 hours later. Bottle wise it's better if you're not in the room and someone else tries. We went through bottle refusal but she has finally started taking one, try to get one nipple shaped - mam are good or lanisoh. I try to do 120ml (think that's 4oz) a bottle, any left we chuck it in her bath. We give at room temp, if I fridge it after I pump we warm it back up in a bottle warmer til room temp or leave it out for an hour or so before her feed. She did bottle feed breast milk first 8 weeks but completely refused the bottle when I started latching her around 2.5 months, every day we try a bottle and the last week or at when she hit 4.5 months she's started taking it again.
I warm up the milk I've pumped in a jug if hot water. EBF babies will typically take 1 to 1.5 oz per hour between feeds so if they fed 2 hours before the bottle then it would be 2 to 3 oz if it was 4 hours then 4-6 oz etc. Pace fed. Also I didnt particularly "pump" just use a Hakka on the other boob every time I feed .