My suggestion: No, do not mix bias-ply and radials.
While there have been a handful of bikes doing just that, the engineers for the manufacturer, working with the tire manufacturer engineers, spent much time to come up with the steering geometry, wheel and tire construction and rubber compounds to make this a safe thing.
Most responsible dealerships won't even agree to mount tires of different types such as mixing bias-ply and radials. If the bike is one of those very few, like a certain H-D, then they would because it says so right on the tire sticker affixed to the bike.
Harley-Davidson Softail Breakout and CVO Breakout were both equipped with a radial rear (240/40R-18) and a bias-ply front (130/60B-19). The Triumph T100, T120, Street Cup and Street Twin are also likewise equipped. (from 2017)
You apparently happened to find a combination of bias-ply and radial tires which you weren't scared silly by mounting/using. I think that's something you should be glad it wasn't a terrible combination. If you choose to repeat it, well, that's your preference, and I wish you well.
I once rode one of the first Japanese literbikes equipped with radial tires from the factory. With the OEM tires, it handled very well as it had an aluminum wide-beam frame. When the front needed replacement, another
radial tire had been mounted, but it was
not the same type of radial tire construction as the rear. The bike suddenly became an evil-handling ride, and when I took it for a ride, I was surprised that different types of radial tire construction could result in such a change in handling, especially when turning. The owner tried to make it work, but finally surrendered and installed the same brand and rubber compound recommended by the manufacturer for the rear and front tires to match. Handling restored.
You're the one who is riding the bike, and I expect you want the bike to perform optimally. My suggestion is that you pick one type, from one manufacturer, and that you choose the rubber based upon how you ride. If you're a long-distance rider, a harder compound will make your tires last longer. However, in my experience with a VMax on both two radial tires, or two bias-ply tires, I prefer a shorter-length tire rubber compound which provides better traction and cornering, as I'm not riding thousands of miles trips.
Here's a link with some info on bias-ply and radials:
https://www.rideapart.com/news/246058/the-motorcycle-tire-question-radial-bias-or-both/
