Xylella fastidiosais an important insect-vectored bacterial plant pathogen with a wide host range, causing significant economic impact in the agricultural and horticultural industries. Once restricted to the Americas, severe European outbreaks have been discovered recently in Italy, Spain, France, and Portugal. The Italian outbreak, detected in Puglia in 2013, has spread over 100 km, killing millions of olive trees, and is still expanding. To date, quantified assessment of important epidemiological parameters useful for risk assessment and management, such as transmission rates, symptomless periods, and time to death in field populations, has been lacking. This is due to the emergent and novel nature of the outbreak and length of time needed to monitor the course of disease progression. To address this, we developed a Bayesian method to infer epidemiological parameters by fitting and comparing compartmental epidemiological models to short snapshots of disease progression observed in multiple field plots. We estimated that each infected tree with symptoms is able to infect around 19 trees per year (95% credible range 14-26). The symptomless stage was estimated to have low to negligible infectivity and to last an average of approximately 1.2 years (95% credible range 1.0-1.3 years). Tree desiccation was estimated to occur approximately 4.3 years (95% credible range 4.0-4.6 years) after symptom appearance. However, we were unable to estimate the infectiousness of desiccated trees from the data. Our method could be used to make early estimates of epidemiological parameters in other emerging disease outbreaks where symptom expression is slow.