For a supposedly ancient individual she appears to be rather naive with some of her actions. Even if what Forestry said about age = power isn't true per se, you would think at her age she would have mellowed down and become somewhat wiser.
How is she naive? The only action she has performed that could be taken as such is brazenly charging at Blackbeard, and we can't even say that action is naive until we know her motivations.
Don't know how old you think she is but it seems like the New World is just as New to her as it is to other worst generation. A lot of people owe their allegiance to Whitebeard and feel indebted to him, he has liberated a lot of countries/islands and claimed them as his territories. Her affection for him could be tied to that
From what we know of Bonney, nothing suggest she is an acolyte in the New World. Granted, nothing suggest she is familiar with it either, and if she isn't, her being the Gorosei's life long slave could explain that lack unfamiliarity; being trapped in Mariejois for an eternity could've prevented her from ever seeing the New World.
She charged Blackbeard, knowing how strong he was; no other character has actually done this outside of the Whitebeard's remnants, and they were his former crew members. Knowing this, Bonney must have some greater tie to Whitebeard than justsomeone who lived in a liberated New World Country. Possibly, she could've looked up to him for being the greatest threat to the WG or something along those lines.
Point being, other than when she stopped Zoro from slicing that celestial dragon, she hasn't been portrayed to be very wise. I'm not sure I believe fully that she is a daughter but like I said it has more weight to it then "slave of the gorosei" just think about it if her connection with the world government goes that far back she probably knows all their secrets and her journey out in the seas seems rather futile
. From what little we know of Bonney, all of her ties either point to the WG or, in one case, Whitebeard. Why would her backstory be oriented around Big Mom when she only has aesthetic ties to the woman, when she already has pre-established relationships with the WG. It just doesn't make narrative sense. You ask why she would escape out to the sea: if she weren't there to reverse the Gorosei's aging, wouldn't her being on the sea have purpose, contrary to what you are saying. Maybe she is one of many in a long line of age devil fruit users that the Gorosei have manipulated, but until such a notion is presented in the manga, I'm inclined to believe she is the sole one. Regardless, Bonney's escape isn't futile.
When you have an ageing ability it's easy to make a joke about the ability user's age, which is what I think that SBS thing was, a joke. Don't hold your breath and expect Bonney to pull a Red Woman on us.
If it was a joke, Oda would've been more clear than simply saying her age was unknown. Regardless, whether or not Bonney is the Gorosei's time slave (as I am suggesting), I guarantee you she is not, in any way, shape, or form, related to Big Mom; Oda would've foreshadowed that idea long ago, but to this day, all we know is that Bonney has ties to the WG and Whitebeard, and as such, that is not the case.