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Using magneto-optical Faraday and Kerr measurements, we investigate the magnetic and magnetooptical properties of a thick Bi-substituted gadolinium iron garnet film over a broad range of wavelengths (250-850 nm) and temperatures (150-300 K), including the magnetization compensation point, TM. We observe an exchange-bias-like effect in the vicinity of TM. By slightly changing the sample temperature, we can precisely tune the bias field, which reaches a magnitude 6 times higher than the coercive field. We explain this phenomenon by considering the short-range superexchange interaction and a change in the magnetic behavior when moving from the surface to the bulk of the film. This finding may lead to the development of single-film magneto-optical devices based on the exchange-bias effect.