(A) I hope the bus comes on time today.

(B) If it comes on time, I won't (contraction for "will not") get to work late.

(C) And if I don't get to work late, my supervisor won't (contraction for "will not") get angry. 

You are writing first conditional sentences for (B) and (C) to describe a future possibility. Your have used your verb tense correctly: the verb for the "if" (subordinate) clause is in the present simple tense, and the verb for the main clause (result clause) has the structure of "will" + present simple tense). 

Just a side comment, first conditional sentences may not always come with an "if clause". For example, your (B) can be re-written as: 

"As long as it comes on time, I won't get to work late."

OR

"And so long as I don't get to work late, my supervisor won't get angry."

These are still considered first conditional sentences to describe something possible at the time of speaking or writing. 

I hope this helps.