Bad moods are common, especially at work. But we don’t say someone has a bad mood. We say that they are ‘in’ a bad mood.
„My boss is in a bad mood this morning“ may sound strange, but trust me, this is a correct sentence.
A different phrase that confuses things is the phrase ‘have a bad temper’. It means that someone is often angry and it doesn’t take them much to explode. Here, a temper is something you ‘have’.
Let’s put the two phrases together:
„My friend has a really bad temper. This morning, he was in a bad mood and when the assistant at Starbucks got his coffee order wrong, he shouted at him in front of the whole cafe!“