When you breathe for air when playing the horn, make sure that you do so, grabbing as much air as possible in the shortest time possible, without changing your embouchure. A good way to do this is though the nose, or on the sides of the mouth, if your mouth is big enough. But it is important that you never 'fall' from a note to take a breath.
What you can do to conserve more air, is to sit at the very tip-corner right side of the chair. Cushions (sofas, loveseats, ect.) are unnacceptable because it is to easy to slouch, even when you do not realize it. So, it is best to play on a actual 'chair', ideally with no backing.
It is often the best to include several breathing exercises in your daily warm-up routine. All are done in common time. When inhaling, make your mouth wider, but when exhaling, make it smaller, so that you have to push air though your mouth. Here are some exercises:
Assume 'b' is beat Assume 'c' is crescendo Assume 'dcr' is decrescendo
Breathe in for 4b, release for 4b
Breathe in for 4b, release for 8b
Breathe in for 4b, release for 12bc
Breathe in for 2b, release for 4b
Breathe in for 4b, release for 10bcd
and so forth.