As I understand "another" - singular, "other" - plural.
No, this isn't true at all. It's a massive over-simplification.
But what makes you think that 'bait' is plural, anyway? It's obviously a singular noun. Don't get distracted by the plural nature of the word 'worms' or the word 'are' - these have nothing to do with it. The words 'another' and 'great' refer to 'bait', not worms.
Look at it this way:
Worms are [another great bait].
Here are some more examples:
Strawberries are another good source of vitamin C.
The Canary Islands are another good place to find winter sun.