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We performed a laser spectroscopic determination of the 2s hyperfine splitting (HFS) of Li-like 209Bi80+ and repeated the measurement of the Is HFS of H-like 209Bi80+. Both ion species were subsequently stored in the Experimental Storage Ring at the GSI Helmholtzzentrum für Schwerionenforschung Darmstadt and cooled with an electron cooler at a velocity of ≈0.71 c. Pulsed laser excitation of the M1 hyperfine transition was performed in anticollinear and collinear geometry for Bi82+ and Bi80+, respectively, and observed by fluorescence detection. We obtain △E(1s) = 5086.3(1l)meV for Bi82+, different from the literature value, and △E(2s) = 797.50(18) meV for Bi80+. These values provide experimental evidence that a specific difference between the two splitting energies can be used to test QED calculations in the strongest static magnetic fields available in the laboratory independent of nuclear structure effects. The experimental result is in excellent agreement with the theoretical prediction and confirms the sum of the Dirac term and the relativistic interelectronic-interaction correction at a level of 0.5%, confirming the importance of accounting for the Breit interaction. [ABSTRACT FROM AUTHOR]