Department Heads & Bridge Officers & Science Sub-Department Heads

There are Department Heads (DH) and primary Bridge Officers (BO) on the Genesis. Examples of this set-up can be found in TNG and Voyager:

Deanna Troi was the only CNS on board, so she was no DH, yet she was present on the bridge in all important situations (sitting in the chair of the second officer no less, because Data sat at the Science station). Ensign Kim was a constant bridge officer on the Voyager and operated the Ops station (which included comms). He often helped with work in both Science and Engineering and reported directly to the XO. Tom Paris was a constant bridge officer at the helm in important situations, but during regular duty he worked as a nurse in sickbay and he helped in Engineering whenever modifications to the Delta Flyer were necessary. He also reported to the XO.
These examples show that it is rather normal for bridge officers to sometimes take part in senior staff meetings. It is also logical, because the bridge officer are the first ones who need to know what's going on in a mission, since they have to react quickly without hesitation of surprise.

The Manhatten class has a unique bridge design (click here to view it). The choice of bridge officers is based also on that. The following are the descriptions of the DH's and BO's:

Department Heads

Department Heads & Bridge Officers

Bridge Officers

Other Swing Positions
(These are not part of the standard senior staff, but are usually present at Senior Staff Meetings)

Science Sub-Department Heads

These are not part of the standard senior staff, but the Manhatten Class is the largest Science cruiser in Starfleet and its Science Department and facilities are so extensive that the CSO can appoint Sub-Department Heads as she/he sees fit, with approval of the CO.
The following Sub-Departments can be filled with a Sub-DH appointment: Sub-Department Heads report to the CSO and are responsible for the labs that belong to their Sub-Department as well as all Scientists that work within their Subdepartment.