i waited for her to pick me up at the airport for like a hour. i realized that she wont pick me up so i caught a taxi and came here.

空港で彼女が迎えに来てくれるのを１時間くらい待った。
でも来ないような気がしたから、タクシーを拾ってここまで来た。

まだ勉強不足なので良い英語で正しく直して欲しいです。
i waitedよりive been waitedを使ったほうがいいのですか？

I had waited for her for about 1 hour as she said to pick me up.
But I came here by taxi, because I felt late and she wouldn’t pick me up. 　

I had waited for her for about an hour at the airport, but there was no sign of her there. So I took a taxi and came here. 　

I had waited for her at the airport for about 1 hour (as she said she would come to pick me up) but she didn’t show up. So I just took a taxi to come here. 　

i waited for her to come and pick me up at the airport about an hour. Then I felt that she may not be coming so took a taxi to get here. 　

もしかしたら間違ってます。修行の身なので訂正お願いします。

I was waiting for her to pick me up at the airport about an hour, but then I realized
she never show up, so I took cab to get here instead.

（相手の家について説明するとき。）
口語でしか英語をならってないので間違ってる可能性大です。 　

それと、待たされた。ってのはできないって事。

http://www.linkage-club.co.jp/Write/items/jyudoutai/jyudotai.html

に書いてあります。 　

この例文には適応できないかもしれませんが、待たされて結局約束をすっぽかされた、という場合は、stood up を良く使います。参考までに。

I got stood up by her. みたいな感じです。 　

I was waiting for her to get picked up at the airport for like an hour, but I just suspected she wouldn’t come. And I decided to take the cab here. 　

上のだったら

I was supposed to be picked up at airport by her, but she never showed up so i decided to take the cab to get here.

では？