Be specific
Name the behaviour you regret and acknowledge its impact. Avoid explanations that turn responsibility into blame. An apology should reflect something you understand, not simply something you hope will restore contact.
Offer realistic change
Describe what you are doing differently without making dramatic promises. Change becomes meaningful through repeated actions over time.
Leave room for their decision
An apology does not require forgiveness or a reply. If contact is unwelcome, respect that boundary rather than using an apology as a reason to bypass it.