As Michael Smith said, "... that she be on time," is correct. More information from Wikipedia. [excerpt] The subjunctive in Modern English occurs in a variety of contexts usually relating to desire or conditional actions. Regardless of the subject, the form of the present subjunctive verb that expresses present or past desires (and other uses) in that clauses is the bare form of the infinitive (not preceded by "to"). Hence, the present subjunctive of "to go" is "I go", "you go", "he/she/it go", "we go", "they go". For instance: "It was required that he go to the back of the line" (compared with the past indicative "Everyone knows that he went to the back of the line"); and "It is required that he go to the back of the line" (compared with the present indicative "Everyone knows that he goes to the back of the line"). The English subjunctive also occurs in counterfactual dependent clauses, using a form of the verb that in the indicative would indicate a time of action prior to the one implied by the subjunctive. It is called the past subjunctive when referring counterfactually to the present, and is called the pluperfect subjunctive when referring counterfactually to the past. It occurs in that clauses following the main-clause verb "wish" ("I wish that she were here now"; "I wish that she had been here yesterday") and in if clauses expressing a condition that does not or did not hold ("If she were here right now, ..."; "If she had been here yesterday, ..."). Source: https://en.wikipedia.org/wiki/Subjunctive_mood#English

The subjunctive is still in use English ; it's just silly to claim otherwise. Its use is more prominent in formal writing and speaking, and in the US than the UK, but what remains is significant, and in many cases the differences between educated and uneducated speech.

Thank you!

'It is important to us that she arrives on time' sounds more natural The second sentence doesn't sound like something that a native English speaker would say. You can use 'be' like this but is sounds old and out of place as we don't use the subjunctive in English any more.

It is correct. Your way is correct too. The use of the older, subjunctive "be" is grammatically correct but now often eschewed in favour of the normal indicative, so "It's important for us that she is on time." In normal life, you can use any of these. If you are doing an exam course, you need a teacher or other access to what the markers on that course expect. I hope this helps. https://www.english-at-home.com/grammar/using-the-subjunctive-form-in-english/