A bike pump will take thousands of strokes to inflate an air mattress. It takes me 15 breaths (about 30 seconds if I don't take any breaks) to fully inflate my medium size (72"x20") NeoAir. I have a hard time imagining it being a big deal to inflate, unless you either have a problem with how you are inflating it or a respiratory problem.
If it isn't a respiratory problem, are you maybe are letting air escape between breaths? or maybe not opening the valve all the way when inflating? Watching others inflate air mattresses I see that a lot of folks let air escape between breaths, that makes it a lot slower and wastes effort. Keep a seal around the valve with your lips and when ready to close the valve, either close off the valve with your tongue or a finger tip. If you get winded easily try giving it one breath, breathing normally for a moment, then give it another, and so on.
There are high volume pumps designed for inflating air mattresses, rafts, or exercise balls. The ones that come with exercise balls are fairly small and light and could be adapted. They would still take quite a few strokes, but much fewer than a bike pump.