Two-fluid flows play an important role in many industrial applications. One attractive property is their ability to induce significant increases in mass and/or heat transfer. Bouncing and sliding bubbles are one of the two-fluid flow mechanisms which are known to give rise to very high heat transfer coefficients in heat exchangers. The present study of the full process of bubble growth, rise, impact, and bounce presents particular challenges because of the interaction between the three phases (gas, liquid, and solid) and in particular at the triple contact line. The present work attempts to answer the following question: "To what extent can the available numerical interface capturing methods and contact line boundary conditions capture the correct behaviour of bubble dynamics under several two-fluid flow processes (bubble growth, detachment, rise, and bounce)?" Three diffierent numerical methods (Volume of Fluid (VOF), Level Set (LS), and coupled CLSVOF) are considered. The wetting dynamics of the bubble against solid surfaces are modelled using both static and dynamic contact angles. The numerical simulations are performed using both commercial and open source softwares (ANSYS-Fluent®-v13, OpenFOAM® , and TransAT©). A simple coupled VOF with LS method (S-CLSVOF) for improved surface tension implementation is also proposed and tested by comparison against the standard VOF solver in OpenFOAM. The numerical results are assessed by comparison against experimental data obtained by a research team at the Fluid and Heat Transfer Research Group in Trinity College Dublin (Ireland) as a part of a collaborative project funded by the Science Foundation of Ireland. The assessment of the numerical results highlights the strong sensitivity of the bubble dynamics predicted numerically on the implemented surface tension model, the interface capturing method, and the Capillary number. The analysis of the bubble dynamics during the bouncing process demonstrates the importance of refining the mesh at solid surfaces in order to capture accurately the bubble behaviour during the collision process