You are disposing of a drive and want to ensure the data is not leaked.
If the data was stored in plain-text (i.e. not encrypted), you would have to ensure the data was 'shredded'. Just formatting the drive would not be sufficient; formatting doesn't overwrite the data, which is why there are 'unformat' utilities.
Instead, you'd consider a tool like DBAN. There are various erasure standards and as @Raystafarian points out, you can be all but sure the data is unrecoverable if you do a 7-pass shred. In truth, there are no reports of successful recovery after even a single pass on a modern mechanical hard drive, but it often pays to be conservative.
Matters are more complicated when considering SSDs. See this article (thanks to @Raystafarian for the link) for more information. SSDs remap blocks, which means you can overwrite all the data on the drive and some of the old data may have been remapped and not actually overwritten. DBAN doesn't handle SSDs.
Okay, but this isn't what you are doing. You have stored the data protected using Bitlocker and aren't planning on shredding or even overwriting the data at all. What you are suggesting is actually similar to how SSDs often implement 'secure erase'. They encrypt all data and then, during the 'secure erase', simply overwrite the block containing the key. Without the key, there's no practical way to recover the data.
This is true in your case, too. You cannot recover the data from a Bitlocker-encrypted drive without knowing the key, assuming no vulnerabilities in the Bitlocker implementation or in the underlying encryption algorithm. The fact that you know a great deal of the plain-text ("known Windows files or known data structures") is irrelevant; the encryption algorithm is strong despite known plaintexts.
In this case, against most adversaries, I'd suggest just doing a complete (as opposed to a quick) format. Even that shouldn't be necessary, but it's probably a good plan. Against a well-funded government or evil criminal empire? Well, you probably have other problems. And then I'd definitely be wiping the drive (using DBAN or a similar SSD-capable tool) and physically destroying the drive.