Pasta is a carbohydrate-rich food with a low glycemic index (GI) and is one of the main sources of slowly digestible starch (SDS). The presence of bran fractions (BFs) in pasta may enhance its health potential, owing to the content of fiber, micronutrients, and bioactive compounds; however, at the same time, BF may affect starch digestibility. In this study, the bioaccessibility of starch in pasta made with BF-enriched semolina (BF pasta), or only with micronized debranned kernel (DK pasta), and a control pasta made with traditional semolina was evaluated by applying two different in vitro models. The control pasta showed a percentage of SDS about four-fold higher than that of the BF pasta and 1.5-fold higher than that of the DK pasta (p < 0.05). The amount of starch released during simulated gastrointestinal digestion was slightly lower, but not significantly different, for the control pasta than for both the BF and DK pasta. These results suggest that the presence of a higher amount of dietary fiber in BF pasta can affect the structure of the food matrix, interfering with the formation of the gluten network, water absorption, and starch granule accessibility, while micronization could enhance starch digestibility due to starch gelatinization. These findings emphasize the need to optimize the process for producing fiber-rich pasta without affecting its low starch digestibility and, consequently, its GI.