Gamma-ray bursts are thought to be sites of hadronic acceleration, thus neutrinos are expected from the decay of charged particles, produced in p¿ interactions. The methods and results of a search for muon neutrinos in the data of the ANTARES neutrino telescope from four bright GRBs (GRB 080916C, GRB 110918A, GRB 130427A and GRB 130505A) observed between 2008 and 2013 are presented. Two scenarios of the fireball model have been investigated: the internal shock scenario, leading to the production of neutrinos with energies mainly above 100 TeV, and the photospheric scenario, characterized by a low-energy component in neutrino spectra due to the assumption of neutrino production closer to the central engine. Since no neutrino events have been detected in temporal and spatial coincidence with these bursts, upper limits at 90 per cent confidence level on the expected neutrino fluxes are derived. The non-detection allows for directly constraining the bulk Lorentz factor of the jet G and the baryon loading fp.