Student or Learner
After I bet (you), we often use a present tense to refer to the future: I bet (you) they don't come (won't come) this evening.
After I hope, we often use a present tense with a future meaning: I hope she likes (will like) the flowers.
The source: Practical English Usage (pages 86-226)
Can't we use a present tense after 's/he bets, they bet, you bet' and 's/he hopes, they hope, you hope'?
Yes, theoretically you can. But you are usually not in a position to tell someone what they bet or hope, or what 'she' bets or hopes.
For example, I am more likely to say, "I hope my reply helps you" than "You hope my reply helps you".
No doubt, this is why the book gives examples with "I bet/hope".