The inclusion complexation of p-sulfonatocalix[6]arene (Calix-S6) with three kinds of phenothiazine dyes was studied spectrophotometrically in a mixture of a room-temperature ionic liquid [bmim]BF4 (1-butyl-3-methylimidazolium tetrafluoroborate) and ethanol. We have determined the association constants of Calix-S6 with phenothiazine dyes under external static pressure up to 767 bar in the [bmim]BF4-ethanol and alcohol-water mixtures. With increasing external pressure, the inclusion equilibrium in the alcohol-water mixtures was shifted to the dissociation side. Conversely, the inclusion equilibrium of methylene blue (MB) and azure A (AA) in the ionic liquid mixture was shifted to the association side. From the analysis of the pressure effects, the reaction volumes ΔV for inclusion complexation were estimated as −7 to 9 cm3 mol−1 in the [bmim]BF4-ethanol mixture and 20–32 cm3 mol−1 in the alcohol-water mixtures. Based on the results, we have suggested that there is a competing complexation between the included dye and [bmim]BF4 molecules in the ionic liquid.