Rapid photobleaching of fluorescent proteins can limit their use in imaging applications. The underlying kinetics is multi-exponential and strongly depends on the local chromophore environment. The first, reversible, step may be attributed to a rotation around one of the two exocyclic C-C bonds bridging phenol and imidazolinone groups in the chromophore. However it is not clear how the protein environment controls this motion - either by steric hindrances or by modulating the electronic structure of the chromophore through electrostatic interactions. Here we study the first step of the photobleaching kinetics in 13 red fluorescent proteins (RFPs) with different chromophore environment and show that the associated rate strongly correlates with the bond length alternation (BLA) of the two bridge bonds. The sign of the BLA appears to determine which rotation is activated. Our results present experimental evidence for the dominance of electronic effects in the conformational dynamics of the RFP chromophore.