If you think that you will be able to get housing that you can have 2 bunnies at- then if you are looking for a friend for Little Bit you could certainly start looking for a suitable bunny and bonding if you find one. If you are unsure if you are going to have to “sneak” or “hide” Little Bit than I might hold off on getting another bunny- it is harder to sneak and hide 2 bunnies.
Little Bit has free run of your room right? Are you going to have some neutral spaces to work on bonding and another area where you could keep a new bunny when it first comes home?
Just be prepared for the poo and pee wars that come with introducing a new bunny into the house. Cotton and Schroeder are just starting to settle after me bringing Griffin home- and I have not been able to even start bonding yet since Griffin is not ready to be neutered yet.
I think if the timing is right and you find an appropriate bunny that suits Little Bit and you- I think another bunny would be an extremely lucky bunny to be able to come live with you and find their forever home.
I know what it is like to think you might have found a littermate- I saw an ad on Craigslist that sounded just like Schroeder- same age, color, breed and already neutered (Schroeder was adopted thru the Humane Society) so I emailed them to find out where they got him from, etc. But he already had found another home. So I totally know what it is like to love one bunny so much that you want to extend that love and care to a littermate!