It seems to me to be pointless laying fibre under your drive... someone is going to need to splice to it at some point, in which case they'd have to dig it up again. And you'd have to make sure it was an exactly compatible type. In fact... I'm not sure BT would want to put a splice there. Isn't that why they're installing manifolds & splitters, to control the places where splices are done?
If you wanted to put *anything* underground, the best bet would be ducting of the right format - so that BT can do whatever they need to with blowing the fibre... but even that is only of use if you can joint it directly to BT's ducting, or accept that it might need to be dug up again anyway.
And all that assumes that
a) You don't already have ducting towards BT
b) That BT will be sending the drop links via ducting rather than overground - no point installing ducts if the manifolds are 30' in the air!
You obviously know about Openreach's "new build" sections. Have you seen their
Developer's Guide?