My unpleasent journey to work these last two days
Normally it is a 30-minute bus ride from my home to my workplace. However, it took more than an hour yesterday morning, when the bus I took was stuck in heavy traffic. It The bus [1] went on moved [1] for a few seconds, stopped, then drove for a couple of mintues minutes, and then stopped again. This drive-and-stop [2] situation lasted for almost 45 mintues minutes. As it was peak time, everyone was in a rush and the vehicles were struggling to move their way for themselves [3], which made the traffic even worse.
At last our bus drove out of the jam and got to the stop where I got off. Of course, I started work late. This morning, to avoid the same situation, I got up 20 minutes earlier. The traffic was good and I arrived at my workplace early.
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[1] The most recent 'thing' you described was the heavy traffic. This means the pronoun 'it' seems to refer to the heavy traffic, and "it went on for a few seconds" suggests that the traffic jam lasted a few seconds. Since this is not your meaning, I have replaced the ambiguous pronoun with "the bus".
[2] A common expression is "stop-and-start".
[3] Sorry, but I don't understand the meaning of this phrase.
Your writing is very good. Your understanding of the use of hyphens and commas is better than many native speakers. Great job!