Once I'm using database mirroring, all my databases has the recovery model set to Full.
When using this recovery model, you must have a good backup policy to regularly backup your transaction log, between full backups of your database. If not, the database transaction log file size may increase a lot.
To shrink the file size I use the following script:
exec sp_dboption DBName, 'trunc. log on chkpt.', true
DBCC SHRINKFILE (DBNameFileName, 500);
exec sp_dboption DBName, 'trunc. log on chkpt.', false