I can imagine that an SPV node encodes the transaction(s) it's interested in, into a BF and sends it to full node. What I don't understand is that what does the full node do after that?
Does it traverse through all the previous transactions and check which one is in the BF and sends it to the SPV node?
Also, it's not clear how private the approach would be, because at the end the full node retrieves what the SPV node wants and sends it to the node, so it knows what it's interested in.
If the goal is to preserve the privacy of the SPV's query, then some sophisticated approaches such as private information retrieval or oblivious ram must be used but they are not efficient for the bitcoin setting.