To cure them more quickly you can either:
- use heat lamps or an electric heater over your resin pieces
- raise the temperature of the room they are in to say, 75 - 85°F / 24 - 30°C.
If you do either of these, you must maintain the heat constantly until fully cured.
Don't be tempted to add more hardener as it can stop the resin curing and remain sticky indefinitely.
There are additives that promote curing (called accelerator) however they are typically yellow in colour so will add a slight yellow hue to the resin. Also, the faster the resin cures, the greater the chance of it yellowing as a combination of the heat by-product of resin curing and heat applied to cure the resin faster.
There are reduced accelerator resins around which are slower curing but cure clearer.
To prevent dust from settling on the resin while curing, you can cover them with a cloche or bowl.
For more info on what I have said, you can read what ArtResin say at https://www.artresin.com/blogs/artresin/44707073-how-to-make-resin-cure-faster