Conformation of six-membered ring constituting a bridged compound
According to structure determined by electron diffraction, norbornane is present in bridged boat conformation. http://pubs.acs.org/doi/abs/10.1021/ja01014a032, see Figure. 



Norbornane and its derivatives are often used for studying effect of equatorial and axial substitution of cyclohexane and is considered rigid. 
Therefore, I don't expect significant population of the second conformer you sketched.

Edit:
For the [2.2.2]bicyclooctane (not the lactone mentioned in question), both conformers are known in crystalographic database. 

Bear in mind, that bicyclooctane constist of three hypothetical cyclohexanes, possibly equivalent by symmetry. 

For any compound of interest, you should find enough data in crystallographic database, but I'd expect all reasonable conformations to exist.