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All answers having "Bye!" as clue:

3 Character Answers:

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RHO



4 Character Answers:

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CIAO

NEAR

TATA



5 Character Answers:

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ADIEU

ADIOS

HUSHA

LATER

SEEYA



6 Character Answers:

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SEEYOU

SOLONG



7 Character Answers:

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CHEERIO

FELICIA



8 Character Answers:

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AUREVOIR

TOODLEOO



10 Character Answers:

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IMOUTAHERE

SEEYALATER



11 Character Answers:

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IMOUTTAHERE