This study proposes a recourse-based robust integrated bidding strategy for multi-energy systems under uncertainties of load and energy prices. A tri-level min-max-min robust problem is developed which is solved through a column-and-constraint (C C) generation technique to recast the min-max-min problem into a min master problem and a max-min sub-problem. Unlike previous conventional dual-based robust models which solved the max-min sub-problem by duality theory, this study employs block-coordinate decent (BCD) technique to solve it, using first-order Taylor series approximation of the sub-problem. The benefit of such approach is that the bidding binary variables can be obtained in the sub-problem as recourse decisions after uncertainty realizations which results in considerably more practical and realistic bidding solutions. This was not applicable in previous dual-based robust models due to the lack of tractability of a dualized mixed-integer model. Another advantage is that the linearization of the dualized inner problem is avoided as Lagrange multipliers are eliminated in this study which results in a more moderate computational time. In addition, it is possible to consider different buying/selling bids for the model as bidding binary variables are modeled in the sub-problem. A comprehensive case study as well as a post-event analysis are developed for an energy hub to illustrate the optimal bidding decisions and compare the effectiveness of the proposed model with conventional dual-based models.