There are different ways and no obvious "best way". It sounds like you need a hydrograph for the road subbasin that has the rain gardens, and that the curb cut itself does not need to be modeled explicitly....
In municipalities that use TR-55/curve number methods, the storage of "IMPs" can be translated into a mean storage depth over the whole basin and then the curve number ratched down accordingly (reference: LID Hydrologic Analysis, Prince Georges County Maryland, July 1999)
In municipalities that use Rational methods, the presence of the rain garden will extend the time-of-concentration for the basin, which in turn will reduce the rainfall intensity used in analyses. This could be determined in an interative fashion, you might find some insight in the City of Chicago storm design spreadsheets.
In municipalities that use continous models, e.g. Washington State, you would have to use the prescribed models and methods of the local agencies, or if guidance is lacking. This is likely to be some sort of detailed level pool routing for a shallow infiltration BMP.