Learn German: Wir haben das Bad gerade geputzt. - We have just cleaned the bathroom.

It comes from the verb putzen (to clean). Because it is a regular (or weak) verb, it follows the standard pattern for the Perfekt tense: add the prefix ge- and replace the infinitive ending -en with -t. So, putzen becomes ge-putz-t.

Why is geputzt all the way at the end of the sentence?

In the German Perfekt tense, the helping verb (here, haben) takes the normal second position in the sentence. The past participle (geputzt) is always pushed to the very end. This creates a bracket around the rest of the information in the sentence (das Bad gerade).

I thought gerade meant 'straight'. What does it mean in this sentence?

You are right that gerade can mean 'straight' (like walking straight ahead). However, when used as a time word, it means 'just' or 'right now'. Here, it tells us the bathroom was cleaned just a moment ago.

Is das Bad in the accusative case here?

Yes, it is! das Bad is the direct object of the sentence because it is the thing being cleaned. Since the word for bathroom (das Bad) is a neuter noun, the word for 'the' stays das in the accusative case, looking exactly the same as it does in the subject position.