Everyday writing
Write an apology with a concrete next step
An apology that ends on feelings leaves the other person to work out the resolution. A concrete next step shows you have thought past the moment and gives them something to respond to.
What to check in the draft
The draft should say what happened, not call it "the situation." Passive phrasing like "mistakes were made" shifts accountability, so check that it uses "I" for your own actions. The next step should match exactly what you said you could offer. If the draft closes with "I hope you can forgive me," it hands the burden back to the reader, so cut or reword it.
After you review the draft
Read the draft once more before sending and remove any detail you did not supply or can't stand behind. Choose the medium the other person would expect: for a serious matter, an email or a call usually fits better than a text.