Plasmid transfer among bacteria is an important driver of the spread of antibiotic resistance. Surface-associated bacterial biomass is a hotspot for plasmid transfer due to the dense spatial packing of cells, but this biomass is often sparse (composed of discrete bacterial colonies). Compared to plasmid dynamics within a single colony, the determinants of plasmid transfer between discrete colonies are less understood. Yet, colonies routinely physically collide with each other as they grow and expand across surfaces. Here, we experimentally demonstrate that collisions between colonies of Stutzerimonas stutzeri and Escherichia coli enable the spread of an antibiotic resistance-encoding plasmid, with the extent of transfer determined by the spatial distance between bacterial inocula. To better understand how spatial constraints influence the mechanisms underlying inter-colony plasmid spread, we applied an individual-based model simulating plasmid dynamics between colliding colonies. Our simulations quantitatively predict how the probabilities of plasmid transfer and loss affect plasmid spread as colonies grow and collide. These effects are modulated by the distances between colonies and the spatial positionings of plasmid-carrying cells along the collision boundary. Our study reveals that inter-colony plasmid transfer is determined by the interplay between plasmid transfer, plasmid loss, and spatial constraints, expanding our understanding of plasmid dynamics in the spread of antibiotic resistance genes.