Which two forms of heat transfer work together to heat water in a plastic bottle

The primary form of heat transfer taking place within the water bottle will be convection, which is the natural circulation of fluid due to density differences arising from temperature differences.

The second form is dependent on how the heating is taking place. If the bottle is out in sunlight, the form of heat transfer is radiation from the sun's rays. If heat is directly being applied to it, then the form is conduction, which occurs in solids and through direct contact.