Short answer
HubSpot's KB: a hard bounce usually indicates a permanent error, though a strict security filter can also cause one. A soft bounce is a temporary problem with the recipient's server. The contact property Email hard bounce reason stores the last hard bounce reason. If the address hard bounced globally but never from your account, that property can be empty.
1. Where to look
Bounce data is in each sent email's performance. My demo portal has five marketing emails, mostly drafts.

2. What to do
- Hard bounce from a typo: correct the email address.
- Hard bounce from a dead address: stop marketing to it. See bounced contacts still marketing.
- Repeated soft bounces: check the recipient's server or your sending reputation.