natalis: That is, “dies natalis”; we will find out by line 2 that it is Sulpicia's, not Cerinthus's, and that it is “invisus” not because she is concerned about her age but because of how she is to spend the day.
rure: Ablative. The locative would not fit here because its last syllable is long: rūrī. molesto: modifies the nearer noun, “rure”, not “Cerintho” in the next line!