I know there is a say 'old habits die hard' but is there also a say 'bad habits die hard'?
The traditional expression, as you rightly say, is 'old habits die hard', not 'bad habits...'.
Other similar expressions:
It's a hard habit to break.
A leopard can't change his spots.
You can't teach an old dog new tricks.
A: You are biting your nails.
B: You can't teach an old dog new tricks!
What will A's reaction be? Does this saying make the conversation funnier, therefore, A might smile back to B?
PS: CJ, thanks for correcting my mistake. I thought 'say' and 'saying' were interchangable.
I have looked it up on the internet. It seems like the saying 'You can't teach an old dog new tricks' means one is slow in learning new skills, while 'Old habits die hard' means one have difficulty in getting rid of one's bad habit.
So, elderly can say 'Don't waste your time teaching me how to use e-mail because you can't teach an old dog new tricks'. Am I right?