Can you ride your bike with no handlebars?

In theory you could. A unicycle operates with no handlebars. So you could try to lean to one side or the other to turn. It would probably be difficult though since the front wheel can turn independent of the back, and if you locked it so it couldn't, you wouldn't be able to turn very fast because of the increased size of the minimum turn radius (one point of contact versus two separated ones makes a huge difference in how fast you can turn). If the front wheel can turn and you want to control it you could either try to reach foward and guide a solid connecting part to the side, which could be both very dangerous and difficult, or you could try to rotate the front wheel with just the tube that connects to the handlebars. The problem is that the tube would have barely any torque against the natural turning of the wheels against the terrain. It would be very, very difficult at best, unless the bike has some points connected to the front wheel which are far from its access of rotation, don't rotate forward with the wheels, and are far enough from moving parts so you fingers don't get caught.