The cryptocurrency system Bitcoin uses a peer-to-peer network to distribute new transactions to all participants. For risk estimation and usability aspects of Bitcoin applications, it is necessary to know the time required to disseminate a transaction within the network. Unfortunately, this time is not immediately obvious and hard to acquire. Measuring the dissemination latency requires many connections into the Bitcoin network, wasting network resources. Some third parties operate that way and publish large scale measurements. Relying on these measurements introduces a dependency and requires additional trust. This work describes how to unobtrusively acquire reliable estimates of the dissemination latencies for transactions without involving a third party. The dissemination latency is modelled with a lognormal distribution, and we estimate their parameters using a Bayesian model that can be updated dynamically. Our approach provides reliable estimates even when using only eight connections, the minimum connection number used by the default Bitcoin client. We provide an implementation of our approach as well as datasets for modelling and evaluation. Our approach, while slightly underestimating the latency distribution, is largely congruent with observed dissemination latencies.