Is it permissible for someone who contributed half of the cost of purchasing a bus to stipulate a certain monthly amount from its profit, or a certain amount if it is rented out?

The questioner did not specify on whom a certain amount of profit is stipulated. If the stipulation is on the partners as a wage for his share, then there is no harm in that. However, if it is in the manner of profit-sharing, then it is not permissible due to its inclusion of ignorance (jahalah), uncertainty (gharar), and harm (darar). Likewise, specifying a certain amount for the rent of the bus is also permissible.