We have used a combination of high-resolution Hubble Space Telescope Wide Field Planetary Camera 2 and wide-field ground-based observations in ultraviolet and optical bands to study the blue straggler star (BSS) population of the outer halo globular cluster NGC 6229 over its entire radial extent. A total of 64 bright BSS (with m255≤ 21.30, corresponding to m555≤ 20.75) has been identified. The BSS-projected radial distribution is found to be bimodal, with a high central peak, a well-defined minimum at intermediate radii (r∼ 40 arcsec) and an upturn in the outskirts. From detailed star counts even in the very inner region, we compute the centre of gravity of the cluster and the most accurate and extended radial density profile ever published for this system. The profile is reasonably well reproduced by a standard King model with an extended core (rc≃ 9.5 arcsec) and a modest value of the concentration parameter (c≃ 1.49). However, a deviation from the model is noted in the most external region of the cluster (at r > 250 arcsec from the centre). This feature needs to be further investigated in order to assess the possible presence of a tidal tail in this cluster.