See that library for e.g:
https://github.com/joshstevens19/ethereum-bloom-filters
You can see that I can check if the Bloom filter contains a smart contract address and if it contains a log with a specific topic.
Now my question:
I would like to check if it contains a log to a specific smart contract. Is it possible? Think about using the Bloom filter to see if there is a specific SC that triggered a transfer.
Is it possible? If I will check both: Transfer event, and the smart contract, I will get many more false positives.
The Ethereum bloom filter contains individual strings separately. It is basically a bag of strings, where only the format of the string distinguishes email addresses, ethereum addresses and topics. There is nothing tying related strings together, so you cannot use a bloom filter in the way you would like to.