So in the case that you end up provisioning a computer or device with Bitlocker, the key may very well end up in a database for query.
Outside of this it's not really so speculative to think that Bitlocker has backdoors for gov't access. It's unlikely that Microsoft Bitlocker survived the combined forces of state-of-the-art cryptanalysis, legal compulsion, and company infiltration (exposed by Snowden).
A backdoor for disk encryption need not directly attack the cryptography. It could be something as simple as a means to generate a bunch of predictable blocks on the harddrive - that's enough to break XTS. That is, even if there's no software backdoors or backdoors build into the TPM (Lenovo, for example, has 'key escrow' capabilities to extract Bitlocker keys out of TPMs) or crypto backdoors in HW PRNGs (e.g. Intel RDRAND), etc there are software bugs in other places that could reveal the contents of the hard disk.
So it's merely not a threat model you're ever going to find a solution for. In the very worst case, presuming there were some mystical level of harddisk encryption that was't trivial to backdoor or break by a sophisticated adversary - intelligence folks can use TEMPEST attacks, break into your computer when you turn it on, and/or get rubber hose access. An encrypted disk will not stop Mossad.
There is no disk encryption that will unilaterally prevent USG from accessing your files (you can only make it more expensive).
But as the USG is fond of repeating - you don't need your disk encryption to protect you from the government unless you have something to hide. You only need it to prevent attacks from criminals and for device theft.