Experience can be earned in both career and custom events (BiLLzuMaNaTi has confirmed that XP can be earned online as well).
You can also farm credits in custom events to use in career mode.
This method nets you a lot of XP (40,000-60,000+) and over 10,000 credits per race. You don't need to complete all the laps, just be the last car standing
You: your strongest car
23 lawnmowers or sofa cars
They do a pretty good job of taking themselves out but you get more XP when you wreck them. Take out the entire field and make sure you have the fastest lap. Then wreck yourself and net those credits and XP!