Information Hovering applies in many applications in Vehicular Ad Hoc Networks, where useful information needs to be made available to all vehicles within a confined geographical area for a specific time interval. A straightforward approach is to have all vehicles within the hovering area exchange messages with each other. However, this method does not guarantee that all vehicles within the hovering area will receive the message due to potential partitioning of the network in areas with low traffic density and/or low market penetration rate. To alleviate this problem in this work we propose a scheme which is based on the application of epidemic routing within the hovering area and probabilistic flooding outside the hovering area. Informed vehicles outside the area can serve as information bridges towards partitioned uninformed areas thus leading to high reachability. A unique feature of the proposed protocol is that it is adaptive in the sense that the rebroadcast probability outside the hovering area is adaptively regulated based on estimates of the vehicle density within the hovering area. We evaluate the performance of the proposed scheme using VISSIM. The reference model used in all simulation experiments represents a section of the road network in the cities of Bellevue and Redmond in Washington. The obtained simulation results indicate that the proposed protocol is successful in satisfying its design objectives and that it outperforms other candidate hovering protocols.