Bicycle pumps are designed for high pressure/low volume whereas air mattresses are the opposite - low pressure/high volume. You won't want to carry any bicycle pump that has enough volume to efficiently inflate an air mattress.

Lots of neat ingenious ways to inflate air mattresses these days, some out of necessity to keep the internal down/synthetic insulation from getting wet from breath moisture. Some use silnylon stuff sacks with a mating valve to connect to the mattress - you loft air into the stuff sack, pinch it closed, and then squeeze the air from the stuff sack into the mattress. Some mattresses have a built-in hand pump in the corner - basically a larger internal rubber bulb with one way valves that work like the old blood pressure monitors. Thermarest has this SV valve which uses the Bernoulli Principle to inflate a larger mattress with 4-5 easy breaths.