Yeah if no one else bets then you have no cash to win so it gets canceled.
Play with your bets on your own character during a race and watch how the odds change. 10/1 odds is basically telling you for every 1$ you win 10$ So if you bet 100 you should win 1000$
The tricky part is that when you look at your odds, they are incorrect until you've actually placed a bet on yourself. So if you see something like 3/5 odds, put 100$ on yourself and see if it changes. If anyone else plunked down a lot of cash it should change and it'll be in your favor.
You of course still need to win OR ensure the person you bet on wins.