Anyone have recommendations if this is a safe way to travel?
Safe, yes. Enjoyable? Thats an individual issue.
Safe, yes. It looks like unless you want to drive or fly, a bus is your best bet. There are direct Flix buses that take about 7 hours. I've used Flix and have been happy with them.
Have you considered the train?
When we were travelling in May 2019, we flew from Cracow to Budapest (and then immediately took a bus to Eger, returning later for a good stay in Budapest). Very fast, not all that expensive.