I found this theory on Reddit and I love it.
So, Clara’s 24 when the Doctor meets her in The Bells of Saint John right? Well, we can assume she was also 24 in all the other instances he found her. And in all these instances she claims to have been there for about a year.
In Asylum of The Daleks she claims to have been trapped on that planet for a year. In The Snowmen Clara took over as governess after the old governess died the previous winter. Finally, in The Bells of Saint John she says she has been with that family for a year.
Perhaps she missed writing “23” in her travel book because she doesn’t remember turning 23.