We have recently reported on the first direct measurement of the 2s hyperfine transition in lithium-like bismuth 209 Bi 80+. Combined with a new measurement of the 1s hyperfine splitting in the hydrogen-like 209 Bi 82+ the so-called specific difference ∆ E = −61.37(36) meV was determined and is in good agreement with the strong-field bound-state QED prediction. Here we report on additional investigations performed to estimate systematic uncertainties of these results and on details of the experimental setup. We show that the dominating uncertainty arises from the insufficient knowledge of the ion beam velocity determined from the electroncooler voltage. Two routes to obtain a cooler-voltage calibration are discussed and it is shown that agreement in ∆ E with the QED calculations and of the hyperfine splitting in hydrogen-like bismuth as reported in the first measurement in 1994 are mutually exclusive.