The imbalance might work against the player in certain circumstances, but playtesting will be required to be certain.
I'd recommend going over the guidelines for Modifying a Class in the DMG pg. 287-288. Perhaps you can find something in there that will let you determine the viability of this class feature yourself. Otherwise, drawing from some of the advice outlined in this section, we have a few steps we can take to explore this feature as a possibility.
Under the Creating New Class Options subsection, it states:
any new option you add should be compared to existing options to make sure it's no more or less powerful, yet remains distinctive in flavor.
Now, looking at the other Sorcerous Origins, specifically those in the PHB, their level 6 features give you an option to expend sorcery points to acquire a specific effect.
The Draconic Bloodline gives you a damage buff to your spells based off your ancestry and lets you spend 1 sorcery point to gain resistance to that damage type. The Wild Magic Origin allows you to use your reaction and spend 2 sorcery points to add a 1d4 to an ally's attack roll, ability check, or saving throw.
Using this home brew feature you would have to expend a bonus action and a number of sorcery points to gain a desired effect. Comparing this feature to what's already available, it seems roughly similar in cost and in terms of balance doesn't seem game-breaking because if you had chosen differently in you Metamagic options you could have otherwise had access to each effect. Basically you're just gaining access to one of these these Metamagic options at an additional cost.
There do seem to be a few issues though,
Quickened Spell When you cast a spell that has a casting time of 1 action, you can spend 2 sorcery points to change the casting time to 1 bonus action for this casting.
You would not be able to use Quickened spell with this feature because you would have already used your bonus action on that turn to gain the feature.
Twinned Spell When you cast a spell that targets only one creature and doesn't have a range of self, you can spend a number of sorcery points equal to the spell's level to target a second creature in range with the same spell (1 sorcery point if the spell is a cantrip).
It seems like the variable cost of sorcery points for this option due to spell level already accounts for the feature's inherent power. Requiring the sorcerer to double the scaled sorcery point cost simply for access to the option, especially at higher levels, seems rather steep and edging more towards the "less powerful" side of things. Imagining a scenario where a 12th level sorcerer wants to use Twinned Spell on a 6th level spell, the feature would force him to expend 12 sorcery points which is the maximum at that level.
Other than these few concerns, and to answer your question, in terms of balance the feature doesn't seem to be overpowered, but when the feature concerns the use of quickened or twinned spell it may in fact be underpowered. But as the DMG says,
Like anything in class design, be prepared to playtest your ideas and make changes if things aren't playing out the way you want them to.
If I am misunderstanding the specifics or the mechanics of your feature, let me know in the comments.