I (45M) lied to my wife (43F) about attending a wellness retreat and now I feel like I betrayed her trust

My wife and I have had a very stable and healthy relationship for 20 years. We've always prioritized open communication and trust. However, I recently made a mistake that has damaged that trust. I signed up for a weekend wellness retreat focused on nutrition and fitness. My wife was supportive, but expressed some concern about a particular female instructor who would be there. To ease her worries, I downplayed the instructor's involvement. At the retreat, I ended up in more group activities with this instructor than expected. Nothing inappropriate happened, but I felt awkward about the situation given my wife's concerns. When my wife asked how it went, I panicked and lied by omission, not mentioning the instructor's involvement. I felt awful about hiding this and confessed everything to my wife the next day. She feels deeply hurt and betrayed, even though nothing actually happened. I lied out of fear of conflict, but ended up damaging the trust in our marriage. I'm committed to rebuilding that trust, but I'm not sure where to start. How can I prove my faithfulness and regain her confidence? Is it fair to ask for forgiveness? I'm struggling with guilt and want to make things right. Any advice would be appreciated.