Timber–concrete composites are established structural elements to combine the advantageous properties of both materials by connecting them. In this work, an innovative flexible adhesive connection in different configurations is investigated. Load-bearing capacity, stiffness, and the failure modes were first experimentally investigated by performing push-out tests. Subsequently, a numerical evaluation using ABAQUS 2017/Standard software was carried out in order to develop a three-dimensional numerical model. The Cohesive Zone Model (CZM) is employed to represent the adhesive characteristics at the contact areas between the Cross-Laminated Timber (CLT) and concrete elements. Three different connection configurations were evaluated, each consisting of five push-out specimens. The study investigates the impact of bonding surface area and the alignment of prefabricated glue strips with the load direction on the connection’s longitudinal shear load-bearing capacity, stiffness, and slip modulus. In addition, the impact of cyclic loads and the impact of time on displacements were analyzed. The average load capacity of the full surface connection (type A) is 44.5% and 46.2% higher than the vertical adhesive strips (type B) and the horizontal adhesive strips (type C), respectively. However, the initial stiffness of the tested joints depends on the orientation of the prefabricated adhesive fasteners, being approximately 20% higher when the bonding elements are aligned parallel to the load direction compared to when they are oriented perpendicularly.