Bubbles are one of the biggest issues we experience when working with epoxy resin. So needless to say removing them can be a challenge. I hope you find these tips useful and enlightening. 
Feel free to also check these 20 Essential Tips When Using Resin

1. ROOM TEMPERATURE

The temperature in the room can affect not only the speed at which resin cures but also the amount of bubbles that are created.
If the temp is too cold then the resin will have more bubbles and can take too long to cure. It can appear milky or cloudy due to thousands of microbubbles. If this happens it is impossible to eliminate all of these bubbles, even by using a torch.
If the temp is too warm then the resin can cure too quickly, not leaving you enough working time.
So ideally try to have your room temperature around 21-24°C or 70-75°F. 

Casting resins have a lower (thinner) viscosity and are not as affected by the cool temperature, therefore tend to have less bubbles. Sometimes though, like when you are doming your art piece, it is better to use a coating resin that has a higher (thicker) viscosity.
If the room temperature is on the cooler side, you can warm the resin by sitting both the resin and hardener bottles in a bowl or tub of warm water. Note: Make sure the lids are on tightly or place the bottles in a plastic bag first to help prevent moisture from getting in to the resin.

2. STIR STICKS

Avoid using wooden paddle pop sticks for stirring the resin, as the resin will penetrate the cells in the wood and release bubbles back into the resin. Plus, the slightly rough surface of the stick also causes bubbles to form as it's stirred through the resin.  Plastic or silicone stir sticks work the best. 

3. MIXING RESIN

Avoid stirring too vigorously as this will introduce more bubbles. Stir slowly whilst carefully scraping down the sides and the bottom of the cup regularly.
Using silicone cups can make it easier when it comes to scraping down the sides and bottom. Some plastic cups cause more agitation with the ridges on the inside.

4. SIT THE RESIN

After mixing the resin let it sit for 5-10 minutes and most of the bubbles should rise to the surface, this is especially for resins with a thinner viscosity. 

5. POURING RESIN

When pouring the resin into the mould or on to your art work, pour slowly and position the cup closer to your project. You will create more bubbles when pouring from a higher distance.

6. ISO ALCOHOL

After pouring your resin, spraying isopropyl alcohol on to the surface of the resin can be a great way to remove existing bubbles. The alcohol breaks the surface tension causing the bubbles to pop. It only takes a light spritz.
Important Note: Do not use a torch after spraying the iso alcohol as this can cause a fire.

7. POP BUBBLES

Use a toothpick or a pin to pop surface bubbles. Simply poke the bubble to pop it, or if that doesn't work, drag the bubble out to the edge of the mould with the toothpick, where you can remove it from the resin.

8. BLOW BUBBLES

Another way to dissipate bubbles is to blow through a straw directly on the bubbles.

9. HEAT RESIN

This is the fastest and most effective method of removing bubbles from resin. Once you have poured the resin you can use one of the following - torch, heat gun, hot air gun or a barbeque lighter to pop the bubbles.
A hair dryer is not the most ideal as it mostly just moves the resin around whilst not really popping many bubbles.
A torch is the most effective but it also is the most likely to melt your silicone mould or damaged the resin from overheating. It does however have an added bonus of removing any tiny dust and dirt particles. Keep the torch moving, not too close to your project, for 1 to 3 seconds. Repeat a few times if necessary.
A heat gun is the better choice if you want to avoid damaging silicone moulds.

Check your project over the next couple of hours, before the resin has hardened too much, and if any bubbles have come back repeat the process. 
Remember to avoid excess heat as it can easily burn the resin or damage the mould.

How To Remove Bubbles From Cured Resin?

Sand your project to smooth out the bubbles. 
Make sure to wash and clean your project with isopropyl alcohol to remove any dust or oils from your skin.
After sanding your piece it will look scratched, but don't worry they will disappear when you apply a new layer of resin.