Want to know if we can make the window size of a bay window larger?
No, no and again NO.  Not the way you suggest it, anyway.

This is an exterior wall.  It is therefore a load bearing wall.  Those two 2x4s (called jack studs) support the header over the window.



The weight of the rest of the house above the window is protected by the header, which in turn transfers the force to the two jack studs (as in they jack up the house) carry that weight to the underlying structure.  If you remove one of the jack studs, too much force may be transferred to the other one, causing it to bow or even possibly fail.  Either scenario translates to having weight of the wall above the house coming to rest on the window itself - and that is a BAD THING (TM).

If you wish to restructure for a larger opening properly, you must open the wall up further and relocate the king and jack studs, and install a longer (and possibly wider) header as well.  Otherwise you can cause many tens of thousands of dollars of damage to your house.

Do not fiddle lightly with structure.