I believe the reason for the manual to recommend Radial tires only is because the speed rating on Bias tires don't match the topspeed of the S10.
Several tire manufacturers have Bias tires specially developed for bikes like the S10.
When running a set of Bias tires, you just have to keep the speed rating in mind to avoid issues.
I have been using Radial tires so far on my bike (Bridgestone BW-502, Continental TKC 70, Michelin Anakee 3 and Pirelli Scorpion Trail II), but as I plan on doing more dirt riding in the future, the time has come for me to try some Bias tires.
I do lots of long distance touring and love how the S10 behaves on tarmac with the tires I've been running up until now. I'm concerned about what I'm giving up in regard of road manners, by switching to more dirt worthy Bias tires - but I have decided to give it a go non the less.
For my needs and the kind of riding I plan to do, I've boiled the options down to the following tires:
Heidenau K60 Scout
Mitas E07 Dakar
Avon Trekrider
Motoz Tractionator GPS
All of the tires on the list will perform much better in the dirt, than any of the Radial tires I've been running.
The first 2 on the list have been on the market for a long time. Both have received lots of praise - and some criticism. My impression is that you will give up quit a bit in regard to on-road handling with either, compared to more road orientated Radial tires.
It have proven very difficult to find reviews of the Trekrider. The few I've found have mostly been very positive, but one was the complete opposite (as always with tires). The thread pattern doesn't look like it will offer a very smooth ride on tarmac, and in my experience this type of pattern will very likely result in significant Heel/toe wear over time (especially on the front tire) - I might be wrong..?
Reviews of Tractionator GPS (not to be confused with the Adventure version) are very positive so far. I havn't been able to find a negative review yet. Besides that a friend of mine are running a set at the moment, and according to him -
https://rtwpaul.com/2018/01/21/tires/ - they feels like street tires on tarmac (both dry and wet). At the same time he find that it offers just as much grip in the dirt as any other 50/50 tire he have tried (with includes Mitas E07 and K60 Scout). It sounds almost too good to be true, but unless I hear something new about the tires before it becomes time to replace the Scorpion Trail II's I'm currently running, I believe Tractionator GPS will be my choice as the first set of Bias on my S10.