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Birch (Betula sp.) bark is a well-known natural source of betulin (Bet) and betulinic acid (BAc), both of which have several bioactive properties. The evaluation of the extraction performance, relative to these lupane-type triterpenoids, provided by different biosolvents requires the development of a high-resolution and high-sensitivity liquid chromatography-mass spectrometry (LC-MS) approach that is also compatible with challenging extractants such as natural deep eutectic solvents (NADESs). In this work, an LC-MS method was developed and analytically characterized prior to its application for the quantitation of Bet and BAc in birch bark extracts obtained using conventional solvents (methanol and acetone) and biosolvents (limonene and NADESs). High precision (RSD < 3.3%), sensitivity (LOD: 23 ng mL−1 and 29 ng mL−1 for Bet and BAc, respectively), and accuracy (95–102% recovery) were found for this optimized method, using an acidulated water–methanol mixture as the mobile phase and sodium acetate as an additive. Extraction experiments conducted at 55 °C revealed that the NADESs, particularly thymol:1-octanol (1:1 molar ratio), outperformed the other solvents and were highly effective for the recovery of both triterpenoids (17.50 mg g−1 and 0.92 mg g−1 of Bet and BAc, respectively). This method can also be applied to similar extracts obtained from other biomasses.