Using the density-matrix renormalization-group method we study the two-dimensional Ising model in strip geometry. This renormalization scheme enables us to consider the system up to the size 300 x infinity and study the influence of the bulk magnetic field on the system at full range of temperature. We have found out the crossover in the behavior of the correlation length on the line of coexistence of the excited states. A detailed study of scaling of this line is performed. Our numerical results support and specify previous conclusions by Abraham, Parry, and Upton based on the related bubble model.