In cases where there aren't enough players to play against in Live Races with Bets, the game may use bots as your opponents. Bots cannot raise bets, so they always play with the base option (200-300 cash).

So if you can't raise, either your opponent doesn't have enough money or he's a bot.

In the Windows version of the game, during Live Races, you'll only encounter a bot opponent. It's a technical restriction unique to this version.