creative writing - Is it okay to say what the character infers about other characters thoughts as fact in third person limited?

The story is third person limited to Bob's point of view. He is with Alice, and I have the following line.

Alice sat up proudly, then shrunk back down, realizing where she was.

Compare this to

Alice sat up proudly, then shrunk back down, apparently realizing where she was.

This is a tiny change, but without it I am technically breaking the limited scope and seeing into Alice's head briefly. But at the same time, Bob could realistically realize that was what was going on in Alice's head, so it does not seem egregious.

The reason I am hesitant to do the second is because I do not want to be constantly hedging statements with things like "apparently" or "seemed to" since it can bog down the writing if used often.

So the question: Is it okay to show thoughts of the non-perspective character if the perspective character can reasonably guess them?

Answer

You seem to have chosen third person limited scope, and then decided that you're "supposed to" follow the rules of third person limited scope. You should make decisions based on what serves the story, not based on whether it's consistent with a label that otherwise applies to your story. If you had some motivation for choosing third person limited, then ask whether putting in "apparently" serves that reason you originally had for third person limited, rather than asking whether it is needed to qualify as third person limited. If you think that distancing the reader from other people serves the story, then put in qualifying words such as "apparently". But if you think the story is better served by being more direct, then be direct.

Also, another option that is somewhat risky as it can erode reader trust, but if done well cements Bob's point of view even more than distancing words such as "apparently", is to give Bob an unreliable POV. If you give narration from Bob's POV, and don't explicitly qualify it as being from Bob's POV, and the narration is later shown to have been occasionally inaccurate, the reader will pick up on the fact that when narration strays into other people's motivations, it has to be taken with a grain of salt. This puts the reader more into Bob's POV, because Bob isn't constantly qualifying his evaluations of other people's mental states. He's not thinking "It appears that Alice realized where she is", he's just thinking "Alice realized where she is". He's making assumptions about what people are thinking, and trying to create a model of their mental states, and occasionally realizing that he was wrong.