We develop bounds on the maximum longitudinal velocity to evaluate the performance and help the design of mobility allowance shuttle transit (MAST) services. MAST is a new concept in transportation that merges the flexibility of demand responsive transit (DRT) systems with the low-cost operability of fixed-route bus systems. A MAST system allows buses to deviate from the fixed path so that customers within the service area may be picked up or dropped off at their desired locations. However, the main purpose of these services should still be to transport customers along a primary direction. The velocity along this direction should remain above a minimum threshold value to maintain the service attractive to customers. We use continuous approximations to compute lower and upper bounds. The resulting narrow gap between them under realistic operating conditions allows us to evaluate the service in terms of velocity and capacity versus demand. The results show that a two-vehicle system, with selected widths of the service area of 0.5 miles and 1 mile, is able to serve, respectively, a demand of at least 10 and 7 customers per longitudinal mile of the service area while maintaining a reasonable forward progression velocity of about 10 miles/hour. The relationships obtained can be helpful in the design of MAST systems to set the main parameters of the service, such as slack time and headway.