This might help
http://www.fictionaddiction.net/articles/contributed/thompsonbio.html
I did mine in first person, and it didn't do me any harm, but maybe it's different for the Brit market.
Good luck.
The Agent I have queried is very specific about the synopsis but there are no clues about how to present the bio. None of the Agent websites I have looked at here and in the UK have mentioned using third person in the bio, so I would be interested if anyone can support this who is published. Mine is currently in the third person but I have to wait until mid-Septemeber before I get a response from the Agent I have queried. They just ask for authors to "query their (Agent's) interest in the project" initially then if the author is lucky, they want three chapters, synopsis and author bio so I have a bit of time yet to work on it.