Eating them isn't a problem. Save $$ on energy bars. Breathing them in, however ...

I don't live in a very buggy area, but as others above have said, I ride with my head bent down, which seems to help. I also have facial hair, maybe that helps to strain some of them out.

MA was requiring masks on the Minuteman for a while. I got about a mile up the path before deciding that the masks I was wearing indoors were completely impractical for riding because they're really not designed to facilitate that much air intake/exhalation. By that time, it was obvious that the virus couldn't be spread that way and I'd already been vaccinated, so I just took the thing off. Indoors, I still followed the masking rules as faithfully as possible.

Long story short--not the same kind of mask, this isn't really relevant. OP is looking for something that filters bugs, not viruses.

Use a trainer inside if you must keep your mouth open while riding. Or only ride in winter months outside.

There was a French rider in Le Tour a few years back who always seemed to be smiling. Turns out that's a pretty good way to cut down on bug ingestion, too. Put your teeth together, pull your lips back, breath through your mouth, and keep on riding.

TBH, I usually only ride that way when I'm crossing a river or marsh at dusk, or when I see a cylinder of insects flying in front of me.

+2

Dawn and dusk are heavy bug times. Riding at high noon probably cuts out most of the bugs.

Sure, but the all the dental floss you'll go through to get the bugs out of your teeth may be cost prohibitive.

Ive noticed I seem to attract more bug strikes when Im wearing a yellow jersey.

Take some chocolate on you ride. Maybe something like Hershey's kisses. Just pop some when you encounter a bug. Makes it taste good.

Another problem with insects entering yoir mouth that has not been mentioned yet - they can make you throw up if they hit you right in the thriat and activate the gag reflex. I haven't actually thrown up this way, but have been close a couple of times. And I have witnessed a person getting less lucky than me once.