Is there anything lower than the bit level of 1s and 0s?
Digital computers work so that (almost) at any given point in time, any wire carries (roughly) one of two possible voltages, one signifying $0$ and the other signifying $1$. The voltages depend on the convention being used. In this sense, digital computing does work with $0$s and $1$s. However, even digital computers interface with analog devices, such as physical storage and networks. The way that data is encoded in networks can be somewhat different, since several bits can be encoded at once, depending on the encoding.

Let me explain my qualifications in the first sentence above. "Almost" refers to the fact that when wires switch from $0$ to $1$ or vice versa, there will be intermediate voltages. These switches are synchronized across all the wires so that whenever wires are "read", the switch (if any) has already occurred. "Roughly" refers to the fact that the voltages are not exact. There are two small ranges of voltages which correspond to $0$ and $1$. The devices should be able to "read" bits throughout these ranges, but usually "write" them more restrictively.