1a. I go to sleep.
1b. I go to bed.
2. Go to bed and sleep.
3. It took me hours to get to sleep.
4a. Children go to sleep quickly.
4b. Children go to bed quickly.
5. Children fall asleep quickly.
6a. I went to sleep because I was tired.
6b. I went to bed because I was tired.
7a. Being tired caused me to go to sleep.
7b. Being tired caused me to go to bed.
Please correct all.

They’r all possible, though 7b is very unusual and 4b is, in my experience of children, not true. They tend to dislike being sent to bed. It marks the end of their ‘playtime’.

These standalone sentences don’t really help in explaining the differences between going to bed and going to sleep, as it is not possible to tell from them whether you understand the concept behind each.