I emailed Ledger and they replied with this:
Thank you for your message.
You can add Burst support request to our roadmap here: https://trello.com/b/5nQ1mdzt/ledger-roadmap
To add a new coin we either need a huge interest from the market, or that the coin's foundation invest in our package.
For information, the "altcoin package" costs 49,000 EUR and includes:
●development of altcoin's Nano S / Blue app
●altcoin support added to the Ledger Wallet Chrome app
●altcoin explorer API development for the backend
●1,000 Ledger Nano S unit with altcoin's logo laser engraving
-- Eric Larchevêque, CEO