I was thinking more of Rickmansworth or Amersham! And I'll warn people who want a hard ride - these are likely to be reasonably leisurely, and mutual encouragement (not least to get out of bed in the first place) may be needed.
There aren't enough bike rides that look at big houses, so here's a draft route that does just that.
http://www.mapmyride.com/routes/view/72532558/
Starting from Amersham railway station, we go first to Chequers to wave at Dave. Then it's along a private estate road (which I need to check out) to the first of several Rothschild properties - Waddesdon. From Waddesdon we go past the railway museum at Quainton to the Verney family residence at Claydon. There is, apparently, a teashop there outside of the National Trust enclave.
From Claydon we skirt back down to Wing, past Ascott and Mentmore (two more Rothschild houses). I've the routed the ride back through Wendover Woods - it wouldn't be a Chiltern bike ride without a long hill, and this is the most pleasant in the area, not least because there's an ace little café at the top. Finally, there's a quick and not-all-that tortuous ride back to Amersham via smaller, but still rather lovely houses in The Lee - including the most surprising bit of public art.
It's about 66 miles. It could be made longer, and still on-theme by including a loop out to Stowe Landscape Gardens (which would mean a picnic in the carpark or by the side of the road unless everyone's an NT member). It could be made shorter by starting at Great Missenden. There are bail-out points a-plenty - the whole route is within a few miles of the Chiltern line out to Aylesbury. Most of the ride is on B or unclassified roads, and there's almost nothing on a busy road. The road up to Chequers is a bit of a drag; Wendover Woods is definitely a hill. The rest is basically rolling.
I'll do some recces, and propose a date.