I know 6/8 is a two feel, so I feel like 12/8 would be a four feel of four triplet groups per bar. Is this correct?
Yep, you're exactly right. 6/8 is to 12/8 as 2/4 is to 4/4.
Now, technically it's not four triplets per bar. The notion of a triplet is that there are three rhythmic units in the space normally given to two of those units; thus a set of eighth-note triplets take up the space normally given to two eighth notes ( = a quarter note). But in 12/8, these three eighth notes combined to create a beat of a dotted-quarter note.
The standard description is that time signatures like 2/4 and 4/4 are called simple meter because their subdivisions are multiples of 2. Meters like 6/8 and 12/8, however, are compound meters because their subdivisions are multiples of 3.