I’m not entirely sure of the reason of your findings, although I’d like to help you with some insights. MB has some aggregate forms depending on its concentration and charge distribution (S+ or N+) on solution. For that reason, different absorption spectra can be seen. Take a look on this work for further details. Article Visible Light Spectroscopic Analysis of Methylene Blue in Wa...
Judging by the fact that ionic SDS and nonionic L-81 give almost the same intensity of the dye absorption maximum, the cause is hydrophobic hydration. This is the effect of changing the structure of the solvent around the surfactant, which affects the intensity of absorption of the dye.
the answer might be quite simple. MB likes to adsorb onto negatively charged surfaces, which might produce some loss. This effect might be reduced adding surfactant giving you always larger absorbance than without.
In accordance with the changes in the spectra of the dye, upon addition of the nonionic surfactant L-81, an increase in the absorption intensity is observed at all wavelengths; therefore, this can be explained by a general increase in the concentration of the dye due to desorption from the walls of the cuvette during the solubilization of the dye in L-81 micelles, as suggested by Sobish. Solubilization is due only to hydrophobic interaction and the formation of an H-bond, so there are no changes in the position of the SDS maxima. In the case of micelles of an anionic SDS surfactant, the solubilization effect can also be accompanied by electrostatic interaction of the dye cation with a negatively charged SDS micelle and a shift in the equilibrium between the monomeric and dimeric forms of the dye. Under the action of a mixture of surfactants, the strongest interaction with SDS micelles prevails, so the effect is the same as when adding one SDS.