"It took me a lot of time" or "It took a lot of my time" both work for me as conversational sentences. Of the two, I think the second sounds better.
from: https://forum.wordreference.com/threads/a-lot-of-my-time.483299/
对比来看，其实这两句表达的意思是相同的。
但是这两句话如果要带着语气说的话，第一句可以强调时间长，第二句可以强调是我。
书面上，感觉第一句更加谦逊。
因为用ME会让人感觉更加谦逊，在翻译“我和你，心连心”这样的歌词的时候，还是特意翻译成了“You and me”。
当然，这是歌曲，为了押韵而已，无可厚非。
但是这里要补充一个tips：
我们说花费时间用take，但很少用cost，实际上，cost后面不能直接跟time，但是可以跟cost sb. time and money。
关于疑问：
it takes sb some time to do sth可不可以改成to do sth takes sb some time或者doing sth takes sb some time?
答案：可以，但是不地道。
你当然可以把目的提前，把to提前，把for提前，但是这样的语序，非常地中式英语。
关于cost：
- the amount of money that you need in order to buy, make or do sth
- the total amount of money that needs to be spent by a business
- the effort, loss or damage that is involved in order to do or achieve sth
- the sum of money that sb is ordered to pay for lawyers, etc. in a legal case
大致可以认为跟钱、损失、代价有关，与“价”不离，用法非常固定。
花时间是：spend time (in) doing sth
还可以是：take sb sometime to do.
没有cost time。
但是我们最常说it takes time，几乎不说it costs time，更不要说it costs me a lot of time。
还要注意一点，不能说it spent me a lot of time，也没有这种说法，不信的话你自己Google一下。
中文要表达「用了时间」可以用花费、耗费、付出、消耗、使用来表示，而英文相对固定，用take。
不要想当然地去用单词翻译的意思去造句，基本上造句造不对的。
惯用法永远要比按语法造句要好。
参考：
https://textranch.com/254634/it-takes-time/or/it-costs-time/
即使是cost time，对比结果是，cost time的time指的是次数，而最后一句
It cost nothing but time and conversation.
确实cost time了，但是更加看起来想表达的是代价很严重，而不是去强调你花多少时间。
所以，我们说：
It takes me a lot of time to do something.
I spend a lot of time (in) programming everyday.
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