Metamagic options specify when you can apply their effect as "When you cast a spell".
Extended Spell When you cast a spell that has a duration of 1 minute or longer, you can spend 1 sorcery point to double its duration, to a maximum duration of 24 hours.
To me, that implies that metamagic is a part of casting the spell, and doesn't require an additional action or bonus action. Otherwise, it would become very difficult to apply any of the effects, and some effects such as Quickened would not be functional (spend an action to use metamagic and a bonus action to cast the spell? Why?)
On the other hand converting sorcery points to spell slots, or spell slots to sorcery points specifically requires a bonus action.
As a bonus action on your turn, you can expend one spell slot and gain a number of sorcery points equal to the slot’s level.
They are special timing effects that do not use an action. As others have said, they can be used when you cast a spell and the only cost is sorcery points.
Metamagic options specify when you can apply their effect as "When you cast a spell".
To me, that implies that metamagic is a part of casting the spell, and doesn't require an additional action or bonus action. Otherwise, it would become very difficult to apply any of the effects, and some effects such as Quickened would not be functional (spend an action to use metamagic and a bonus action to cast the spell? Why?)
On the other hand converting sorcery points to spell slots, or spell slots to sorcery points specifically requires a bonus action.
If you needed to use an action or bonus action for meta magic, you'd never be able to use meta magic since spells also cost actions/bonus actions.
As a rule, if an ability requires any kind of action, it will explicitly say so in the description.
They are special timing effects that do not use an action. As others have said, they can be used when you cast a spell and the only cost is sorcery points.