Bidding for upgrades is fairly common these days and many airlines do it, primarily in Europe. Typically there is a minimum bid that's fairly substantial.
Whether this is worth trying or not depends on your own preference. I won a $400 bid on a Tap Portugal flight from Boston to Lisbon. It's an overnight flight - Tap Portugal flies a really nice lie-flat configuration on this route. The $400 saved me food and drink cost in the airport and I was much better rested and functional the next day in Europe.
I did not bid on the return flight, since this was a pleasant afternoon flight and to me the extra money wasn't worth it.
If you like business class flying, bidding is a way to save money. A US->Europe business class ticket on TAP is probably around $3000 and an economy is maybe $600. If you bid $500 each way and get it, you get the business class for $1600 or about half the price.
As I do not really care what class I fly in
Then don't bid.
Is it usual that you can only bid more than the ticket had cost when you bought it or have I missed my chance on bidding a small amount by waiting a day or so?
They typically don't allow a small bid. The minimum bid (at least on international flights) is pretty substantial.