“Bonus turn” does not mean that their TM is automatically filled to 100%, which is a common mistake people believe.
A bonus turn happens immediately after the action performed. For example, if an enemy gains TM to 100% as a result of an attack, but your ally has a bonus turn mechanic, they automatically take the next turn no matter what... I may be mistaken, but I don’t think there are any exceptions (assuming the character taking a bonus turn isn’t stunned/fractured)
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Tentatively, though, I think the answer is "no."
A bonus turn happens immediately after the action performed. For example, if an enemy gains TM to 100% as a result of an attack, but your ally has a bonus turn mechanic, they automatically take the next turn no matter what... I may be mistaken, but I don’t think there are any exceptions (assuming the character taking a bonus turn isn’t stunned/fractured)