Steady-state and time-resolved fluorescence behaviors of two dipolar solutes, coumarin 153 and 4-aminophthalimide, have been studied in an alcohol-functionalized room-temperature ionic liquid, 1-(hydroxyethyl)-3-methylimidazolium bis(trifluoromethanesulfonyl)imide. The steady-state fluorescence parameters have been exploited for the estimation of the polarity of this ionic liquid and to obtain information on the hydrogen bonding interaction between the ionic liquid and the probe molecules. The time-resolved measurements have been focused on the dynamics of solvation by studying the dynamic Stokes shift in the ps-ns time scale and solute rotation by measuring the time dependence of the fluorescence anisotropy. The time-resolved anisotropy studies reveal a significant slow down of the rotational motion of one of the probe molecules. The time-dependent fluorescence Stokes shift measurements suggest that the time-resolvable part of the dynamics is biphasic in nature, highly dependent on the probe molecule and the ultrafast component is comparatively less than that in other ionic liquids. The influence of the hydrogen bonding interaction between the probe molecules and the ionic liquids on the solute rotation and the various components of the solvation dynamics is carefully analyzed in an attempt to obtain further insight into the mechanism of solvation in these novel media.