We used Hartsholme Park, reviewed on here. The Warden told us where we could park the 'van which was just outside the town at the top, and we walked down from there. However there are reviews that talk about bus stops and cycling in too.
Don’t know when you want to go, but the Lincoln show at the end of September is only £43 from Thursday to Monday and only about 10 minutes to Lincoln. There is a shuttle bus on the Saturday. Cheaper than a site and you have the show and entertainment thrown in.
Nora
Don't forget to leave a review of the campsites you have visited this year or last!