Yes it can be combined as long as you don't use two hands to make an attack with a weapon
Bladesong don't have limitations on what you are holding in your hands:
Starting at 2nd level, you can invoke a secret elven magic called the Bladesong, provided that you aren't wearing medium or heavy armor or using a shield. It graces you with supernatural speed, agility, and focus.
You can use a bonus action to start the Bladesong, which lasts for 1 minute. It ends early if you are incapacitated, if you don medium or heavy armor or a shield, or if you use two hands to make an attack with a weapon. You can also dismiss the Bladesong at any time you choose (no action required).
Nothing specifies you need to have one free hand or anything like casting a spell so as long as you don't attack with it while holding the weapon you are ok.
You are descended from a master of the double-blade, and some of that
mastery has passed on to you. You gain the following benefits:
• Increase your Dexterity or Strength score by 1, to a maximum of 20.
• While wielding a double-bladed weapon with two hands, you gain +1
• A double-bladed scimitar has the finesse property when you wield it.
Only wielding the double-bladed weapon with 2 hands is required for Revenant Blade to proc (the +1AC).
- To respond to one of your comment: Sword burst is legal because it has only verbal component, however any spell with a somatic
component would make you lose the Revenant Blade benefit because
you need to hold the weapon with 2 hands.
- You can put your hand back on your weapon as a free action if you are further away you could just hold the weapon in one hand (losing Revenant Blade benefits of a +1 AC for a moment) cast a spell with a somatic component, then put your hand back on the weapon to gain Revenant Blade effect back (Bladesong would still be active and at the end of your spell you'd be fine)
- It's worth noting that a double-bladed scimitar has the Two-Handed
property, so you can't attack with it unless you're holding it in
both hands – @nick012000