Bits' transmission in links
No, you don't have to wait until the bit has arrived before sending the next one. A signal will travel at about 2/3 of light speed in vacuum in a wire, that's 200 000 km/s, or 20 m in 100 ns. A bit every 100 ns is 10 Mbps, and there are many systems which go faster than that. At 100 Mbps the first bit will be 2 m down the cable before the next one starts.

The 


  how long it takes to transmit each bit of data  


refers to the transmitter only, and ignores the travel time through the cable. At 1 Mbps you start sending the first bit at time zero, and the next bit will start at time zero plus 1 &micro;s, no matter how far the previous bit is in the cable. A system with ten times that throughput will start the second bit at time zero plus 0.1 &micro;s. I'm saying "throughput" and not "bandwidth" because they're not exactly the same. The 1 Mbps signal may use the same bandwidth as the 10 Mbps signal, if the latter is allowed to have some edge distortion for instance. A higher bandwidth will give a more accurate representation of the original waveform, though the medium (the cable) may also deteriorate that.

A higher voltage allows the signal to go further in terms of the resistance it meets, but it won't travel faster. Note that you don't need electrons to send a signal: in optical fiber it's photons that do the job.