Yes, you can move before taking the bonus action attack

No timing is specified

On your turn, when you score a critical hit with a melee weapon or reduce a creature to 0 hit points with one, you can make one melee weapon attack as a bonus action.

The phrasing here says nothing about the precise timing of the bonus action. It can be simply read as saying that after the condition is met (critical hit or reducing to 0 hp) that you are granted the ability to make a bonus action attack. It never says the bonus action must be taken "immediately" or anything along those lines so the timing of the bonus action attack is not restricted at all.

You choose when to take a bonus action during your turn, unless the bonus action’s timing is specified

The rules for when you can take a bonus action say that if the timing is not specified, then you can choose when to take it. Thus, there is no reason why you would not be able to choose to move before taking the bonus action attack.

The rules explicitly allow moving between attacks

If you take an action that includes more than one weapon attack, you can break up your movement even further by moving between those attacks. (PHB 190)

Even within a single Attack Action, the rules allow one to move between attacks. It absolutely makes sense that they would allow it between an Attack and a bonus action attack for example. After all, even if the bonus action isn't considered to be part of the Attack action (or whatever triggered the GWM bonus attack condition), it is indeed a weapon attack and thus moving between them seems like an incredibly reasonable interpretation.

Jeremy Crawford has agreed this is the intended interpretation

Jeremy Crawford has clarified this exact issue via Twitter and agrees with the interpretation above:

The intent is that you could move before taking the bonus action in the Great Weapon Master feat.

Each combatant gets 1 action, a bonus action if they have a power to use it, a reaction and movement equal to their racial movement ability.

The rogue has way too many actions.

On action 1, do they have advantage or a buddy in melee? If so then they get SA. Action 2 if they have used SA, they don't get it again. Their bonus action is used to make this attack (see note below, this cannot be done with the longsword). Action 3 is impossible as they have no actions remaining. Action 4 is permissible, though it would provoke an opportunity attack. The rogue is left with some remaining movement but nothing else to do.

Also unless your rogue is human, and has taken a feat at L1, it cannot attack with TWF using a longsword. TWF requires light weapons be wielded in both hands.

So we have:

1. Action: attack
2. Bonus action: attack with off hand weapon
3. invalid, both bonus and regular action used.
4. Ok, but eats opportunity attack
5. invalid, both bonus and regular action used.