Path-based transaction (PBT) networks, which settle payments from one user to another via a path of intermediaries, are a growing area of research. They overcome the scalability and privacy issues in cryptocurrencies like Bitcoin and Ethereum by replacing expensive and slow on-chain blockchain operations with inexpensive and fast off-chain transfers. In the form of credit networks such as Ripple and Stellar, they also enable low-price real-time gross settlements across different currencies. For example, SilentWhsipers is a recently proposed fully distributed credit network relying on path-based transactions for secure and in particular private payments without a public ledger. At the core of a decentralized PBT network is a routing algorithm that discovers transaction paths between payer and payee. During the last year, a number of routing algorithms have been proposed. However, the existing ad hoc efforts lack either efficiency or privacy. In this work, we first identify several efficiency concerns in SilentWhsipers. Armed with this knowledge, we design and evaluate SpeedyMurmurs, a novel routing algorithm for decentralized PBT networks using efficient and flexible embedding-based path discovery and on-demand efficient stabilization to handle the dynamics of a PBT network. Our simulation study, based on real-world data from the currently deployed Ripple credit network, indicates that SpeedyMurmurs reduces the overhead of stabilization by up to two orders of magnitude and the overhead of routing a transaction by more than a factor of two. Furthermore, using SpeedyMurmurs maintains at least the same success ratio as decentralized landmark routing, while providing lower delays. Finally, SpeedyMurmurs achieves key privacy goals for routing in PBT networks.