To solve this problem, we need to establish the conditions that lead to the correct number of bus stops in the city given the requirements for the bus lines. Let's break down the problem and find a systematic way to achieve the solution.

### Conditions:

1. Each line passes exactly three stops.
2. Every two different lines have exactly one stop in common.
3. For each two different bus stops, there is exactly one line that passes through both.

### Step-by-step Analysis

Let's denote the number of bus lines by $l$ and the number of stops by $s$.

1. Each Line Has Three Stops:
- This means for $l$ lines, there are a total of $3l$ incidences of stops on lines (since each line connects to three stops).

2. Every Two Lines Share Exactly One Common Stop:
- Consider any two lines: They intersect at exactly one stop.

3. Exactly One Line Passes Through Any Two Stops:
- For any pair of stops, exactly one line passes through both. This implies that if there are $\binom{s}{2}$ pairs of stops (ways to choose two stops from $s$), there are $\binom{s}{2}$ lines, because each line corresponds uniquely to a pair of stops.

### Solving for $s$:

From condition 3, we establish:
$$l = \binom{s}{2} = \frac{s(s-1)}{2}.$$

From conditions 1 and the definition of incidences, the total number of line-stop incidences, $3l$, must also equal the number of unique stop pairs each line connects:
$$3l = 3 \times \frac{s(s-1)}{2} = s(s-1).$$

This is consistent with what we derived from condition 2, but let's verify by calculating potential small values to find feasible integer solutions for $s$ and $l$.

### Checking Small Values for $s$:

We find solutions in some simple quadratic cases:
1. **If $s = 3$:**
- $l = \frac{3(3-1)}{2} = \frac{6}{2} = 3$.
- This implies there are three lines each connecting three stops. Full connectivity conditions satisfy these numbers, considering the system described.

2. **If $s = 7$:**
- $l = \frac{7(7-1)}{2} = \frac{42}{2} = 21$.
- This number gives a broader possible connection system.
- Often equated with a properties known within projective planes (a classical configuration often referring to this design being feasible).

Hence, the possible numbers of stops (solutions for $s$) that satisfy the city requirements are:
$$\boxed{3, 7}.$$

Thus, this setup allows for either a smaller or a more complex design of bus stop connections - both satisfying the conditions provided from the problem statement.