A possible way to study the reionization of cosmic hydrogen is by observing the large ionized regions (bubbles) around bright individual sources, e.g., quasars, using the redshifted 21 cm signal. It has already been shown that matched filter-based methods are not only able to detect the weak 21 cm signal from these bubbles but also aid in constraining their properties. In this work, we extend the previous studies to develop a rigorous Bayesian framework to explore the possibility of constraining the parameters that characterize the bubbles. To check the accuracy with which we can recover the bubble parameters, we apply our method on mock observations appropriate for the upcoming SKA1-low. For a region of size $gtrsim 50$ cMpc around a typical quasar at redshift 7, we find that $approx 20$ h of integration with SKA1-low will be able to constrain the size and location of the bubbles, as well as the difference in the neutral hydrogen fraction inside and outside the bubble, with $lesssim 10%$ precision. The recovery of the parameters are more precise and the SNR of the detected signal is higher when the bubble sizes are larger and their shapes are close to spherical. Our method can be useful in identifying regions in the observed field which contain large ionized regions and hence are interesting for following up with deeper integration times.
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