If I have dual wield both the fighter skill and the feat, can I swing with a longsword and then use my bonus action to throw the net.

Two-weapon fighting requires light melee weapons, the feat only removes the light requirement, it still has to be a melee weapon.

Quote from Lunali >>

Two-weapon fighting requires light melee weapons, the feat only removes the light requirement, it still has to be a melee weapon.

 Because a net is a ranged (not melee)  weapon,  you cannot use it RAW..

Thanks