I brought several bites of a banana./ I cut the apple into bite sizes and ate some of them.
ご質問ありがとうございます。
① "I ate a banana./ I ate an apple."=「バナナ(1本)/(リンゴ1個)を食べた。」
② "I ate half of a banana./ I ate half of an apple."=「バナナ(1本)の半分を食べた。/ リンゴ(1個)半分を食べた。」
③ "I brought several bites of a banana."=「バナナを何口か食べた。」
"I cut the apple into bite sizes and ate some of them."=「リンゴを食べるサイズに切って、その何個かを食べた。」
ご参考までに。