You are right! Compost is the best thing to use but I figured you didn't have access to such large amounts. Shredded wood mulch will be the next best thing as it will prevent erosion and further compaction so the Bermuda roots can grow back in right away. If you can spread a little compost, even half an inch, it will help enormously.
I know sand is typically used but regular sand settles into its own little pocket and causes problems later on. That's the source of many drainage and water absorption problems on golf courses! These pockets also collect poisons...not nice.
So put down a little compost and a lot of mulch and you should have a happy yard by June!
Kathe