You won't save money, but you might be able to use the "Buyer Agent Fee" as a negotiation tool. If you "self-represent" on the buying side, you will also have to be prepared to coordinate the purchase agreement process, and title company process.
I'm not sure how much you know about the process, so sorry if this is redundant, but I thought it might be interesting for others. Typically a seller agrees to pay a brokers fee through their "Seller Agent" which is then split 50/50 with the "Buyer Agent". A seller can negotiate this fee with their agent, though it's often somewhere between 5-6% of the purchase price. If we take 6% as an example, typically 3% will go to the Seller Agent, and 3% will go to the Buyer Agent, thought that's also up for negotiation between the two agents.
Buy self representing on the buyers side, you can effectively negotiate 3% back to the seller as part of your offer.