There are two main providers of public bus services on Mallorca
EMT who provide the city bus routes in Palma.
And, as the question poser highlights, TIB which is the authority that provides bus services across the island.
In the city ‘officially’ EMT will only allow buses on board if they are the folding type
However I have seen people on buses with a bike in the wheelchair space. I guess they would be asked to get off if a wheelchair user needed the spot.
Bus services provided by TIB are actually operated by a number of different companies under licence or contract. And as such means that the are a great number of different bus types. Most of which don’t have a dedicated bike rack or luggage space.
On longer routes such as the ones from Palma to the North and east of the island the service is operated by larger Coach / National Express / Greyhound Type vehicles which have a luggage boot/trunk underneath. I have seen bikes being placed in this space, but there is no means of securing the bikes, so there is a danger of them sliding around. The placing of any luggage / bikes in the storage space is at the discretion of the driver.
In short. City / local buses – officially- folding bikes only
Longer distance coaches. All depends on the vehicle and available space. No specific prohibition, but most definitely at your own risk. And no guarantee that a specific or suitable vehicle will be allocated to any particular service.
Mallorca is an amazing island to cycle, and whilst not in your question, it’s worth mentioning that many car rental services do have bike boxes to rent for an additional fee on top of the car rental price.