Hi Norris,
There are two aspects to your question – what speed is safe for your bearings and what speed is safe for your chuck, pulleys and other rotating parts. With large cast iron body chucks there is a danger of bursting them due to centrifugal force. However, this probably will not be a big worry with your relatively small Zyto lathe. When in doubt though, increase speed gradually and stay out of the way while doing so.
For the bearings there is an excellent pocket guide for calculating the PV factor (the main determinor in bearing design) at the following link. It gives max recommended speeds in feet per minute for three kinds of babbit. It would be safest to use the speed number for the lowest grade, as you don't know exactly what grade you have. This number is 800 fpm. To calculate the max rpm at this V value, use their equation V(800 in this case) = (pi/12) x RPM x shaft diameter in inches. Using your spindle dia as shaft dia and solving for RPM will give you some idea of a safe speed.
**LINK**
Hope this info helps.
JD