The short answer to the question is: we are not told. However, several things can be gleaned from the text: Pharaoh was going to the water: This suggests two things
- The river was not in flood and because Pharaoh had to move to the river.
- The fact that Pharaoh was predictably going to the river suggests one of two possibilities. Either (a) Pharaoh was going to the Nile to have his regular morning ritual ablution (Compare Benson's notes. This is unlikely but not impossible - compare Ex 2:5), or, (b) it was an annual festival, 120 days after the initial river flood when the Nile receded and the new fertile soil was apparent.
If this latter more probable idea is true, Pharaoh would have been accompanied by a significant retinue of attendants and officials making Moses' message have much greater impact.
Several commentaries reach a similar conclusion:
He cometh forth to the water.—It is conjectured that this was on the
occasion of the great autumn festival, when, after the retirement of
the Nile within its banks, and the scattering of the grain upon the
fresh deposit of mud, the first blades of corn began to appear. It is
not improbable that Khepra, “the creator,” was then especially
Cometh forth to the water - See the Exodus 7:15 note. It is not
improbable that on this occasion Pharaoh went to the Nile with a
procession in order to open the solemn festival, which was held 120
days after the first rise, at the end of October or early in November.
At that time the inundation is abating and the first traces of
vegetation are seen on the deposit of fresh soil.