Let's see :
Kamen Rider literally means Masked Rider, so a Rider with a Mask.
Old Generation Riders use Bug masks/motif/helmets
New Gen Riders : basically anything.
Here's the list after Kuuga and Agito (I'm sure you guys categorize them as Bug-Looking or Bug-Eyed, and they both resemble the older riders)
Ryuki is a dragon, and he rides a huge bike (I forgot the name, Ride Shooter or something?) to enter the mirror world. He is bug-eyed, but his helmet has a dragon motif and he has a dragon symbol and visor.
Kabuto is a beetle, and he also has a bike. He has a bug motif for the sake of Kamen Rider's 35th anniversary.
Hibiki is an Oni, he gets his bike somewhere in the middle of the episode. He is masked (Oni-style). Doesn't this make him a Kamen Rider?
Faiz has a "Phi" helmet, his bike can beat the **** out of someone. The Phi symbol gives him a bug look.
Blade is also a beetle plus a knight armor and the Spade symbol .His bike has a Spade symbol as well
Den-O wears a halved peach helment, from the legend of Momotaro. What's the matter with "not-rider-like" with Den-O? He has a bike as well, can be used outside and inside the train. Ep. 21 -22 : Den-O vs Zeronos , both of them use their bikes and they shoot each other. Ep. 32 : Bike duel with an Imagin. Ep. 27 : U-Ryotaro chases a thief with the bike. Ep.2 : Den-O uses the bike already. Which part of "Kamen Rider" doesn't fit in Den-O, in a literal sense?
(and all of them have horns/antennae/something pointy on their helmets)
It's funny to see that no one talks about Amazon. He is a lizard, he has a unique bike, and no one complained. How about KR Shin? Yes, he is a motorcycle racer and he is a grasshopper mutant. You cannot get anymore grasshopper than that, but he never use his bike in mutant form. No henshin for him... he turns into a grasshopper mutant literally.
Is this just a "Old Gen > New Gen" bias or what?
They have a different storytelling. They have different themes. Deal with it. You cannot use an idea of someone being turned into a Kaizo-Ningen for 36 years, there needs to be a change.
Also, is it really a must to have a bug motif everytime a new Kamen Rider appears? I say NO. The idea of Faiz could be traced back when Ishinomori Shotaro was still alive. The particular idea was to have a Rider using a cellphone-like device to henshin.
What is the difference between the "not-bug" Kamen Rider and a One Man Super Sentai? Ridersare more individualistic and they usually rely on their bikes. Den-O is a breakthrough on this tradition by using trains.Super Sentai is about a GROUP of heroes plus gigantic mechas and tighter suits.
Kamen Rider is about someone who tries to save the world and meet the other Kamen Rider which may have a different perspective and perhaps, a different goal to achieve. In the past days, all the Riders are heroes. Now, you have villainous Riders who use their powers for their own benefit. Some of the idea comes from the big bad Shadowmoon himself.
EDIT : You can satisfy your bug-rider appetite by watching KR The First and the Next. The gods of KR have appeared once again in theatres.