Aper is described here as a sacerdos, priest, which could denote both a presbyter and a bishop. It seems, however, that if Aper had indeed been a bishop, his see would have been mentioned. It would also be highly unusual for a bishop not to live in his city; furthermore, Aper is seldom visiting cities (in plural) and there is no mention of his flock feeling abandoned, which could be anticipated to be otherwise.
Paulinus sent letters 39 and 44 to Aper as well, both of which are addressed to his wife Amanda. These letters, which seem to predate the one presented here (presumably written after the death of Amanda, since she is not mentioned), picture Aper and Amanda as an exemplar Christian couple. Having fathered multiple children, Aper separates from his marital bed and spends his days on prayers and pious studies. Meanwhile, his wife tends to their multiple estates.
Of the three extant letters of Paulinus to Aper, this is the only place where Aper's ecclesiastical office is mentioned.
It is impossible to date those letters with precision, but they were all written after 397 (one of them incorporates fragments of Augustine's letter to Paulinus from that year) and, most probably, before 407 when Vandals, Alans, Suebi, and other tribes invaded Gaul and the connection between Gaul and Italy was severed.