One other thing - the baby is having to use her/his tongue to slow the flow of formula from the bottle. This is a different way of using the mouth. Basically the baby is doing everything possible to avoid being engulfed by the formula coming out of the bottle.
It was beyond heartbreaking for me to see my sweet babies nurse for hours and then gulp down their supplement bottles. When I talk to moms dealing with this type of issue I always try to remember to allow space for them to address the feelings of rejection, fear, panic even, that come when the baby appears to be so much more interested in the bottle than in mommy.
FWIW my story on supplementing is long and tedious, but I was able to ditch the dratted bottles at 9 months (Ali) and 10 1/2 months (Anni). I still hate bottles and formula more than just about anything on the planet. There is just absolutely nothing worse than feeling like your baby prefers plastic and corn syrup to you.
And - we're still nursing constantly not to say incessantly at 2 years. You can go through the hell of supplementation and still CLW, you really can!

IMO this is one of the most difficult things about the use of bottles and formula - we spend so much time talking about the risks to health, but the damage to mother's self-confidence and the mother-baby relationship when this "gulps down the bottle" thing happens is really really awful. I suspect it's one of the things the bottle/formula makers count on. Sigh...