Bugcrowd's company blog covers bug bounty programs, security research, vulnerability handling and hacker interviews.
HN commenters link it for advice to bug bounty hunters, including note-taking methods and the legal risks of testing systems without permission.
Here's a blog post that offers advice: https://blog.bugcrowd.com/problem-cold-testing/
tl;dr The laws aren't going to side in your favor. Assuming this is a US-based airline, there are potential laws you should be aware of (Computer Fraud and Abuse Act & another one). But from this very high level, it sounds like you did a good job of cooperating and not disclosing it "inappropriately".
It just ends up rubbing people the wrong way to come out asking for a reward. If they have a program like this already, they will reward you. If they don't, this isn't going to be what convinces them to start one.
There's a blog post on Bugcrowd about note taking techniques. Might be helpful for you! :) https://blog.bugcrowd.com/the-importance-of-notes-session-tracking-bug-bounty-hunter-methodology