At no point does this bitcoin have to live in the BTC wallet of you, your bank, your friend's bank, or your friend. In fact, this BTC can be entirely fictional. As long as your bank has enough BTC in their actual wallet that they are at no serious risk of running out if a realistic proportion of their customers wanted to withdraw their BTC, as determined by the Fed or other national entity, then all is well.
This is anyway the only realistic possible use of BTC itself, as the blockchain is far, far too slow to use for day to day transactions even in a large village/small town. I can also promise you that this is exactly what day to day use of BTC in El Salvador will look like, more or less, if they do go through with it.
Edit to add: the dollar was once based on gold. We've moved on from that after realizing that doesn't work. Today's dollar is very much not tied to gold, and it is used in ways gold is not.