If you're not a bloodrager (blood sanctuary) and you don't have the centered spell metamagic then no I don't think you can get such a bonus.
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You can't cast Burst of Radiance with your eyes closed as you need to see the target point.
In some instance, the GM can give you a circumstance bonus to the saves against your spells if you can take some action to mitigate the effect, but it is a GM call and generally you are limited by the need to take an action between the casting and the spell effect.
If you are dropping Burst of Radiance on a small area that includes yourself, I don't think you need to see the target position in order to do that.
On the other hand, there is no defined benefit to doing that -- Nothing in the spell description indicates that you are resistant to the blinding effect if you are not looking at it.
Combat in the game is an abstraction and that cuts both ways. Combat is broken up into rounds and discrete turns to make it easier to manage. In the game only one thing is happening at a time, but what it is supposed to simulate is everything happening at once. When you cast your spell a lot of things are going on around you and you need to be aware of them or your character is helpless. If you want to close your eyes (give yourself the blinded condition) it should last for your turn.
The spell description does not say how long the lights last, but from the fact that you are dazzled even if you make your save I would say it is more than just a single flash. They probably last a second or two, which means just closing your eyes when the spell is cast is not going to work. You would need to keep them closed for longer and during that time you would be blind.
So here I am, with the opportunity to hit 3 opponents without hitting any of my companions with a Burst of Radiance, all without having to cast defensively... if, of course, I am willing to drop it on top of myself...
It won't do me any damage ( I am good), but it could blind me. Given I'm the one casting the spell, and I know the exact timing of the flash, is there anything can I do in the rules to give myself a save bonus (closing my eyes at the right moment for example).
Fun story, I was in this exact position, except it was 5 enemies (goblin rogues), and I was on a horse.
I dropped the Burst of Radiance on myself. I passed the save, the horse passed the save, and all 5 goblins failed.
Have faith my child and ye shall be rewarded.
But seriously, no you don't get any bonuses against your own spells. This spell is already the Beez Kneez, don't try to argue it should be better than it is. Bloodragers get Blood Sanctuary , or you can take Selective Spell or Centered Spell but otherwise you just have to trust the dice gods.
Assuming you have more than 1 eye, your GM could allow you to close 1 eye when casting the spell and then opening the non-radiated eye afterwards, all in all maybe a small bonus on your saving throw against Blinded but doubling the resulting Dazzled penalty.
If you want to do this more often, try playing an Elf with the Lightbringer racial trait: immunity to light-based blindness & dazzle.
Even if you get blinded, you should know the terrain to be able to run behind your party after you cast it, or you could move before it and just take an AoO or two (assuming you weren't taking AoO's beforehand because of casting defensively).