The Doctor’s reported age is very inconsistent, something which is well documented elsewhere on this site:
I won’t bother to recap everything those answers cover, but various answers proposed include:
- The Doctor just doesn’t know or remember
- The Doctor is lying
- He de-ages or the age of a Timelord doesn’t work like that of a human (timey-wimey wibbly-wobbly)
To address the specific question of Season 6, I think it’s plausible that two centuries have actually passed between The Impossible Astronaut and The Wedding of River Song. What we see on screen isn’t the entirety of the Doctor’s adventures, with or without companions.
References are often made to escapades they’ve had which occur off-screen, and a particularly pointed one occurs in The Impossible Astronaut, when River and the Doctor compare diaries:
River: Alright, then. Where are we? Have we done Easter Island?
The Doctor: Um… yes! I’ve got Easter Island.
River: They worshipped you there. Have you seen the statues?
The Doctor: Jim the Fish.
River: Oh! Jim the Fish! How is he?
The Doctor: Still building his dam.
I think we’re meant to believe that 200 years have occurred off screen, and that we only get the edited highlights, so to speak. (As another example of the Doctor travelling for a long time, off screen, without a companion, witness the Tenth Doctor going off for a year when he’s summoned by the Ood.)
It’s unclear as to whether it’s exactly 200 years, or whether that’s an exaggeration to make a point, or an approximation, but I do think the Doctor has spent a good chunk of time travelling between the two episodes.