But what I can’t seem to understand is how the ledger transmits data to the blockchain saying “I’m sending 2 bitcoins to a public key.” Without accessing those private keys. Like it only transmits signed transaction data?? What is that.
Ok... so going back to your original post, it seems like what you're actually thinking is "how the Ledger can "sign" a transaction, without accessing the private keys?".
The short answer, is that it can't... it absolutely MUST access the private keys. However... the trick to the Ledger is that it has the "secure element". This is basically a mysterious "black box" containing all your private keys... the black box can see/access your keys... but no one else (including you) can. So, the idea is that you put in an unsigned transaction... the black box does "magic black box stuff"™ and a signed transaction comes back out.
You can't see what is in the box, you can't access what is in the box... the box will only accept an unsigned transaction
[1] as input... and will only give a signed transaction (or error) as output. It has a bunch of inbuilt code and functions and magic smoke that allow it to achieve this wizardry... but due to Non-Disclosure Agreements and lot's of secrecy... the only people that actually know exactly how the internals of this black box work are the manufacturers.
Hopefully that helps...
[1] - In case any pedants are here... yes, I know it will also accept "messages" for signing.