Is there any way I can use regular dremel bits on a dremel trio?
Dremel don't support that
Here are the reasons they give:

Q: Can the Dremel Trio use Dremel rotary tool accessories?
A: No. Though Trio accessories look and work like standard rotary tool accessories, they are specially engineered to handle the demands placed upon them by this slower yet more powerful tool.
Q: What is the difference between rotary tool and Trio Accessories?
A: The Dremel Trio only accepts accessories with 3/16” shanks. Rotary tools, on the other hand, use accessories with shank diameters ranging from of 1/8” to 1/32”. This means you can’t use Trio accessories in your Dremel rotary tool – and you can’t use rotary tool accessories in your Trio (and there are no “conversion collets” available allowing you to do so).

The rotary tools have high speed (e.g. 30,000 RPM) but low-torque motors. Maybe the Trio is different and might break bits designed for low-torque tools (or at least, Dremel wish to avoid being held responsible for any consequences of large numbers of bit breakages)