You can find examples in standard dictionaries for both “I bet” and “I'll bet” used in this sense, though “I bet” is more common. In our opinion, “I bet” (present tense) sounds more natural when the subordinate construction is in the past tense (“I bet she felt crummy”) or the future tense (“I bet he'll forget”).
Johnson decided to launch his own cable television network. Johnson would soon acquire a loan for $15,000 and a $500,000 investment from media executive John Malone to start the network. The network, which was named Black Entertainment Television (BET), launched on January 25, 1980.