The stability of thermocapillary flow in a liquid bridge under a transverse rotating magnetic field (RMF) was numerically investigated by the linear stability analysis using the spectral element method. Three commonly used RMF models, namely, the infinite model, the simplified finite model and the Φ1-Φ2 model, are employed to describe the RMF and their results are compared. Additionally, for the Φ1-Φ2 model, the uniform and non-uniform RMF were also compared. The numerical results show that with the increase of magnetic Taylor number Ta, the critical Marangoni number (Mac) for the three RMF models increases firstly, then decreases sharply to a minimum, finally increases again when the RMF is strong enough to suppress the radial and axial convection induced by thermocapillary force. Two transitions between the wavenumber k=1 and k=2 mode are observed with increasing Ta. The results obtained by the simplified finite model are in good agreement with those of the Φ1-Φ2 model, however, the infinite model has a significant deviation compared to the Φ1-Φ2 model. Besides, the results indicate that the non-uniform RMF has a relatively weak action compared with the uniform RMF.