Bitcoin is a decentralized currency system that does not need any central authorities. All transactions issued by users have been recorded in the common ledger, called blockchain, which is shared by all users. In Bitcoin, an SPV (Simplified Payment Verification) client, which is a lightweight client that does not possess the entire blockchain, are developed for storage constrained devices such as a mobile phone. For an SPV client to check if there are transactions related to it, a Bloom filter where their Bitcoin addresses are involved is sent to a full client that possesses the entire blockchain. The full client only transfers transactions of which Bitcoin addresses are positive on the received Bloom filter. However, it is necessary to preserve the privacy of SPV clients when designing a Bloom filter because SPV clients' Bitcoin addresses will be identified by a full client with high probability. In this paper, we propose a privacy-preserving Bloom filter design for SPV clients based on γ-Deniability. γ-Deniability is a privacy metric that shows how much true positive Bitcoin addresses are hidden by the false positives in a Bloom filter. Furthermore, in order to design a Bloom Filter that satisfies a certain γ-Deniability, it is necessary to know the number of unique Bitcoin addresses that appear for the first time since the queried time. Based on our manual inspection, we propose to estimate it based on the linear regression. We show that our scheme achieves good estimation accuracy and γ through the simulation with a real Bitcoin blockchain.