If I understand this correctly, Bitbills has a great system, but they only hold the Private Key, and not the whole Wallet.dat file?
If by 'they' - you mean the card, not the company - then yeah.. seems right so far.
Each bitbill holds the private key only (hidden so that revealing it wrecks the card). There is no longer any corresponding 'wallet'.
The corresponding address is printed openly on the card so you can verify in the blockchain that the card is worth it's face value.
If I understand correctly, this means all wallets are actually held by bitbills, correct?
I don't think it makes sense to say this.
When buying bitbills you're trusting that they keep no copy of the private key.
If this is correct so far, then how come someone doesn't just place the whole wallet file on a data storage card, then the whole bitcoin will be contained right there, essentially?
Then, when you trade cards, you actually trade the bitcoin.
Am I way off the mark? Would this not work?
That'd work. But there's no need for a whole wallet.
This is the same for their bank card, correct? You can load and reload the card, but the wallet.dat file is still kept on their servers. So, this is ultimately unsafe, correct?
As above - no wallet or private key is kept for the bitbills or their bank cards... assuming we trust bitbills to have a secure process of generating the private key and ensuring nobody takes a photo of it etc.
Lose the card - any money loaded on it is lost forever.
I think it's a good bet that bitbills is trustworthy in this regard - in that even one proven violation would potentially ruin their business.
I would like to see more contact and business information on their website though.
EDIT: In short - the bitbills company could go out of business - and your bitbills cards would still hold the bitcoins just fine.