Alara is the Worf equivalent for The Orville and his role was also Chief of Security.
That includes not on security personnel but the security of the ship also (at least in these contexts). That would require her to be aware of any potential threats to the security of the ship as a whole.
Obviously the most logical place to do that is on the bridge with the rest of the senior staff.
Bortus' actual responsibilities are less well defined but as Second Officer we can assume his role (in that position) is similar to that in Star Trek
The second officer of a starship assumed command of the ship when both the captain and first officer were unavailable. Typically a second officer on a Starfleet vessel held the rank of commander or lieutenant commander. It was common for a second officer to be a department head aboard the ship first, since the role of second officer was considered a nominal position. He or she was rarely involved in the day to day command of the starship or starbase the way the captain or first officer was.
Again, although not generally involved in the day to day running of the ship he is also required to be on call as it's common in the show for the Captain and First Officer to both leave the ship on away missions.
Granted it's likely that these Department heads actually have their own offices (at least I believe that this was true in Star Trek) but, out of universe, limited set availability and the requirements of keeping your actors on screen to "get your money's worth" probably dictates here.