If it's a private rental minibus, usually not. It's not illegal to drink alcohol as a passenger in a vehicle, but it may be against the regulations of the company that operates the bus. Around 80% of bus operators allow alcohol to be brought on board, but will often require a deposit or cleaning fee for any possible dirt. It's best to consume canned beverages and plastic cups, as most suppliers prohibit barrels or glass bottles to keep the coach clean and safe.
As long as the bus provider allows it and you keep the bus clean, safe and legal for underage passengers, carrying alcohol on board shouldn't be a problem. Different people will reach this limit after a different amount or type of drinks; a strong cocktail will have more effect than a cider, for example. If you live in the state of California, you must designate a companion over 25 years of age for all underage passengers because of the AB 45 bill, which requires companies that operate party buses to control alcohol consumption among minors.