Not at all. The "hydrogen" in hydrogen bombs is in deuterium (proton plus a neutron) and tritium (proton plus two neutrons), both isotopes of hydrogen. Deuterium is stable, but tritium is not. Tritium must either be maintained as it decays (into Helium 3) by topping it off or bred in the nuclear explosion itself from lithium capturing a neutron. In either case, the source material is contained in the bomb itself, so you can initiate the bomb anywhere.

Also, the atmosphere contains almost no hydrogen (except a little bit in the form of water vapor).