YOU SAID:

I woke up at around 3:20 am just to go back to sleep then woke up at 5:50 am to get ready for the bus!

INTO JAPANESE

私はちょうど眠りに戻るために午前3時20分ごろに目が覚め、バスの準備をするために午前5時50分に目が覚めました！

BACK INTO ENGLISH

I just woke up around 3:20 am to get back to sleep and woke up at 5:50 am to get ready for the bus!

INTO JAPANESE

午前3時20分ごろ目覚めただけで眠りに戻り、5時50分ごろに起きてバスの準備をしました！

BACK INTO ENGLISH

I just woke up around 3:20 am and went back to sleep, got up around 5:50 and got ready for the bus!

INTO JAPANESE

私は午前3時20分ごろ目覚めて、眠りに戻り、5時50分ごろ起きてバスの準備をしました！

BACK INTO ENGLISH

I woke up around 3:20 am, went back to sleep, got up around 5:50 and got ready for the bus!

INTO JAPANESE

私は午前3時20分ごろ目が覚め、眠りに戻り、5時50分ごろ起きてバスの準備をしました！

BACK INTO ENGLISH

I woke up around 3:20 am, went back to sleep, got up around 5:50 and got ready for the bus!