Use Wiha “Micro Bit” bits with regular 1/8” hex screwdriver

I think the bits as basically very low quality. When you go to your favorite store, simply buy one of the contractor grade of bits like DeWalt, Kolbalt, Irwin, Vermont American etc. Be careful what kind of jobs you tackle with your light duty screwdriver. I'm sure it does not have the power to drive longer screws into hard woods like decking etc. You have to hold a lot of force against the screw in these situations or the bit will slip, spin and dull, as well as strip out the screw head.

Pull it straight out the opposite way it went in. The retaining ring is a spring steel circle of round wire that is split on one side. The diameter of the circle is very slightly smaller than the distance around the points of the 1/4" hex bit:

The ring is inserted so that it floats inside of a groove around the inside end of the driver tool socket.

When a bit is first inserted into the tool socket the rounded fillet on the back end of the 1/4" hex bit is designed to allow the ring in the groove to expand out around the hex bit.

Just as the bit reaches its full insertion depth the ring is allowed to drop into a series of notches that are machined into the corners of the bit all the way around:

This is what helps to keep the bit from falling out of the tool socket. Sometimes with a new tool where the ring has not been exercised much it can clamp into the grooves extra hard. Another factor is that some hex bits have deeper notches which may also enhance the grab the ring has on the bit.

The normal thing to deal with this situation is that the insertion and removal of bits needs to be done a few times to relax the spring steel ring some. At first it may be necessary to use a pair of pliers to extract the bit. A small amount of lubricant could help too.....but it is not recommended for several usage scenarios. One example is if the tool is being used around raw unfinished wood the lubricant can stain the wood in an undesirable manner.

Note that not all hex bits have the retainer ring grooves. The retainer ring can still help keep such bits from falling out of the tool socket but the retention is based purely on the friction against the bit as opposed to the snap action of the notches on the bit.