Suppose high voltage is used to represent 1 and low voltage is used to represent 0. How are the bits transmitted over the wire?
Bit values are only one half of the problem, the other is timing: the receiver needs to know when the bits happen, when one bit ends and the next one starts, etc. If the receiver gets a waveform like this:
then it wouldn't mean anything without the red lines below, which represent the time points when the bit value is meaningful and should be read:
One solution is to transmit a bit clock on another wire (like I2C or SPI) to tell the receiver when it should sample the incoming bits. That solves the bit timing problem, but that doesn't solve the other problem, which is... what do the bits mean? If the receiver needs to extract meaningful information from the bits, for example to combine them into bytes, characters, frames, packets, etc, then it needs to know which bit is the first one in one of those units.
This can be solved with another wire, like a word clock in I2S or chip select in SPI, which tells the receiver which bit is the first bit, ie when a frame starts.
So, a serial protocol that transmits raw bits over the wire, as voltage levels, needs at least 3 wires. But if you want to use less wires, then the above information has to be encoded into the data stream.
For example, in I2C, only two wires are used, and framing information (start of transaction, etc) is encoded by transitions that don't occur during normal data transmission.
In most other source-synchronous protocols (that means one separate clock line) like HDMI, framing information is encoded in the data.
Serial UART only needs one wire. There are start bits to signal when the transmission starts (solves the framing problem) and the user sets the baud rate manually to the same value on both ends, solving the timing problem.
So even if raw bit values are transmitted on the wire encoded as voltage levels, like in Serial UART/RS232, they're not the only thing being transmitted. There's also framing and timing.
Most systems don't transmit bit values directly, but use symbols instead. This can be anything (frequency, phase, amplitude levels, bit encoding, etc) that suits the transmission medium. For example you could use 4 voltage levels to encode 2 bits. In this case, there are no bits on your wire, only symbols.
For example, Ethernet. It's a layered system with each layer using the layer below. Suppose your browser makes an HTTP request. It is encapsulated into TCP/IP packets, which are then encapsulated into Ethernet packets, each layer adding its own information saying what the data means, where it should be routed, etc. This is passed to the Ethernet MAC/PHY chip (or pair of chips), whose job is to transmit this data to the other side of the Ethernet cable. In 100Mbps mode (the usual 100BaseT) it first converts the data to 4b5b encoding, which means each half byte (4 bits) is encoded into a 5-bit sequence which has some desirable properties, like avoiding long sequences of identical bits: since no clock is transmitted, the receiver has to extract it from the data by looking at the transitions between bits/symbols. If a long sequence of identical bits was transmitted, then there would be no transitions, and the receiver clock would not be able to realign with these transitions, so it would drift, and maybe miss the next bit when it comes. Some of those symbols also encode start conditions so the receiver knows where the packets start.
Encoding frame boundaries requires extra transmissions, it can't be done inside the original bitstream: if you define that a certain sequence marks the beginning of a frame, then when that sequence occurs at random in the transmitted data, it would be interpreted as frame boundary. The 4b5b encoding solves this problem along with clock recovery.
Then this is further encoded into analog modulation and sent on the wire. Note the modulation scheme is independent from the previous step. Optical ethernet and copper ethernet use different ones.
Can multiple bits exist on the wire at an instant of time?
If you use symbols that represent several bits (like 4 different voltage levels) then yes.
If you use symbols that represent less than one bit then you could have less than one bit on your wire.
If the wire is long enough relative to the symbol rate, then it is a transmission line. For example with USB3 at 5 Gbps, take a propagation speed of 200000km/s, then the signal propagates about 20cm in one nanosecond. With a rate of 5 symbols per nanoseconds, this means each symbol is about 4cm long in the wire. So if the wire is 1 meter long, there are about 25 symbols propagating in it. Each one represents slightly less than one actual data bit due to the encoding being used, but you get the idea.