I understand your frustration and would suggest you shop around for a bottle nipple that baby likes. There are different shapes and sizes (we loved Advent) but sooner or later you'll find one. When you buy a nipple, smell it = ick! = your baby feels the same way. So wash it and then put it in your brassiere for a few hours so it has your scent/taste when you try to transition. Then, when you're ready, you can try the new nipple. If it doesn't work, try another nipple another day.
You could try giving the bottle first thing in the morning (which means you've slept with the nipple all night) when the baby is ravenous -- that could make it easier for him/her to take it over the breast -- HOWEVER, since the baby is only 3 mos old, if s/he gets red-faced-angry, I would stop and try again at a later time.
But perhaps the easiest way would be for someone ELSE to give the bottle for the first few times -- that would be least confusing to Baby who has associated your scent with your breast and when you introduce something else s/he's saying "wait a minute, that's not right." So, if Dad or Grandma is around, that might be the way to go, and then it won't be so confusing when it's your turn!!!
Good luck, and happy feeding!

I think Theresa has some excellent advice. It will take some trial and error....and some patience. Hang in there Mom!

It can also be temperature of the milk or formula. Warming it up a few times if you're baby is a slow feeder, and over time slowly transition the baby to eventually to room temperature. Another reason why the baby may not like the bottle is not the bottle itself, but the positioning itself; breast feed babies like the pressure of you against their front. I used a wide folded bath blanket with a room temperature gel cold pack inside, and placed it on my babies tummies while my husband fed them. He was getting quite a complex when they didn't like him feeding them.

It's true about trying out different nipples until you find the one that works. Baby bottle comes in either the tradition width (like by EvenFlo) and wide (like Advent). Since you already have a bottle, just change out nibbles that can work on your bottle before moving on to a while new set up.

Devilk's advoate: If this three month old is still lucky enough to have mama's milk, I would not be imposing a bottle unless I had really, significantly addressed the issue that once the bottle is tolerated it may completely take preference over the breast. If this is simply a gesture to give mom a break, as it seems, there may be oter, wonderful, tolerable ways in which to do so that do not upset the baby's natural and normal attachment to the current nursing routine. Offer to do laundry, go grocery shopping, or play with the baby while Mom takes a shower....those are much appreciated ways to give a real break!!!