I currently have a level 6 Dragonborn Goolock with Pact of the Tome, and I'm thinking of leveling into wild magic sorcerer. I've got a thematic reason for it, but I was wondering when to start leveling and how much. I mainly want it for the ability to cast Eldritch Blast twice, so it needs to be at least 3 levels, but I don't know if I should go anymore and forsake my Mystic Arcanum.

You already get two beams from EB as a 5th level Warlock and EB isn't viable for Twinning because it is able to be used against different targets.

Eldritch Blast can target multiple creatures, and is therefore ineligible for use with Twinned Spell Metamagic.

Sorry, should have clarified. I'm planning on casting it twice using Quickened Spell and casting it once for an action and another for a bonus action.

Okay. Just remember, as soon as you decide to cast anything as a bonus action, the only other spells you can cast that turn are cantrips.

Ask your DM to let you search for Illusionists Bracers instead. That lets you cast a cantrip twice in one turn, once as an action and a second time as a bonus action. 

Quote from IamSposta >>

Okay. Just remember, as soon as you decide to cast anything as a bonus action, the only other spells you can cast that turn are cantrips.

 luckly eldrich blast is a cantrip!