We feed and do naps on demand. We don't have a set routine (and probably a 3 month old won't easily fall into one), but by about 4 months, she was generally starting to do things at similar times each day (give or take an hour or so). Her needs are always changing, which is why I think having a set routine is difficult. You might want to schedule in 5 bottles a day, but with a growth spurt, your baby might need 6 or she might drop back to wanting only 4. That screws up the whole schedule and I think can be really stressful for some people. But they will eventually settle into doing things roughly similarly day-to-day (though that might change week to week or month to month). It will at least be similar enough to what happened yesterday or 3 days ago, if that makes sense. Unless you are someone who only functions with a set routine (and there are lots of people like this, which isn't necessarily bad), I'd just go with what she seems to need and work out what seems best from there.
Around 3 months, I think our daughter was having 6 bottles or so a day (had just switched over from BF) and was napping 3-4 times a day. Now at 6 months, she has about 5-6 bottles a day (usually around 8am, 11am, 3pm, 6pm, 8pm, sometimes at 4am, etc, plus or minus an hour or two.) and naps 2-3 times (about 5 hours total). She usually gets tired about 2 hours after she starts a feed, though it can also take 2 full hours for her to eat as she's a really slow eater, so sometimes she goes right to sleep after!
