Rift Valley fever virus (RVFV) is a (re)emerging mosquito-borne pathogen impacting human and animal health. How RVFV spreads through a population depends on population-level interactions between hosts and vectors (e.g., vector-to-host ratio and biting preference) and also on potential differences in individual following virus exposure (e.g., transmission efficiencies from host to vector and vice versa). Here, we estimated the probability for RVFV to transmit to naive animals by experimentally exposing lambs to a bite of an infectious mosquito (the transmission efficiency) and assessed if and how RVFV infection subsequently developed in the exposed animal. Aedes aegypti mosquitoes, previously infected via feeding on a viremic lamb, were used to expose naive lambs to the virus. Lambs were either exposed to 1-3 (low exposure) or 7-9 (high exposure) infectious mosquitoes. All lambs in the high exposure group became viremic and showed characteristic signs of Rift Valley fever within 2-4 days post exposure. In contrast, 3 out of 12 lambs in the low exposure group developed viremia and disease, with similar peaks in viremia as the high exposure group but with some heterogeneity in the onset of viremia. These results suggest that the likelihood for successful infection of a ruminant host is affected by the number of infectious mosquitoes biting, but also highlights that a lamb can be infected by a single mosquito. The per bite mosquito-to-host transmission efficiency was estimated at 28% (95% confidence interval: 15 - 47%). We subsequently combined this transmission efficiency with estimates for mosquito life traits into a Ross-McDonald mathematical model to illustrate scenarios under which major RVFV outbreaks could occur in naive populations (i.e., R0 >1). The model revealed that for efficient RVFV transmission relatively high vector-to-host ratios as well as strong feeding preference for competent hosts are required. Altogether, this study highlights the importance of experiments that mimic natural exposure to RVFV. The experiments facilitate a better understanding of the natural progression of disease and a direct way to obtain epidemiological parameters for mathematical models.