C7/Bb = C/Bb Slash Chord on Guitar

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Slash-Chord. On the left side of the slash you have a chord, on the right side the lowest tone (bass).

The [1]7/[7] (say „[1] over [7]”) consists of the tones [1] (1), [3] (3), [5] (5) and [7] (7). Since the bass on the right of the slash does not necessarily be part of the chord symbol on the left, the [1]7/[7] can be seen and notated as a basic [1] major chord with a [7] played in the bass. Depending on the context (chord progression) you may prefer either notation. You'll find [1]/[7] and [1]7/[7] with about the same frequency.

Example chord progressions:
[7]  [1]/[7]  [b3]/[7]  [4]/[7]
Here different major chords are played over one static bass note („pedal bass”). The notation [1]/[7] is favorable here.

[1]  [1]maj7  [1]7/[7] …
respectively
[1]  [1]maj7/[maj7]  [1]7/[7] …
In this case the notation [1]7/[7] helps to recognize that the major 7th (maj7) is descending to a minor 7th (7). When playing a guitar solo that for sure can accelerate the decisions which scales, arpeggios or guide tones to play. For [1]maj7/[maj7] and [1]7/[7] you can even use chord shapes, where the root [1] is not even played anymore, because all tones [1] of the first chord shape descend by half-steps ( C → B → Bb ).

Here another chord progression:
[1]  [1]7/[7]  [4]/[6]  [b6]
Ok, one more...
[1]  [1]7/[7]  [6]7   [2]m7  [4]m6  [1]