It's not the most cost-effective method when you first unlock her shop, but once you hit World Tier 8 or 9 and start receiving more Epic items, you can start selling all your Unusual or Rare gear to exchange for Titanium.
Upgrading a piece of Lv 30 gear from Rare to Epic costs 50 Titanium, which you can purchase from Bailey for ≈16K scrap.
Though you won't want to do this to the first few pieces of Epic or Legendary gear you find, once you hit endgame, you shouldn't get too attached to subpar epic or better gear that can be disassembled to get Titanium needed to upgrade the items you really care about