Bureau Alerts are the time-limited missions that randomly pop up. You'll know when one is active, it'll flash up in massive yellow letters and an annoying alarm will blast out.
It's worth doing this before you finish the main story line, as I think they spawn a bit more infrequently once you've completed the game.
Edit to include comments: jakubzazula says you should start to get them about 30 minutes after you've completed the main story.
WhoIsJohn117 recommends doing some side missions if you've completed the game and they're not appearing after this time.
You'll have 20 minutes to complete each Bureau Alert (the remaining time is tracked in your mission menu). If you die during the 20 minute window, you'll fail that Alert.
They're not too hard. Track the mission from your menu, fast travel nearby and go for it. Objectives vary but include:
- protecting FBC agents
- clearing out enemies
- destroying small destructible blocks of red hiss crystal...stuff
If Bureau Alerts aren't appearing
If you aren't getting any alerts appearing at all, UnmatchedBrace recommends completing the 'Put a Record On' side mission. This may make them start appearing again.