Hmmm Base DC of 15 (10 for 4' wide + 5 for slippery) - but that doesn't take into account the unstability - after all it's a rope bridge not a suspension bridge so as a judgement call you could apply a further +5 making it 20. So far so good.
However there are ropes to hold onto, making the balance check easier - so perhaps apply a bonus to the balance check for holding onto the ropes (players should not need to state they are doing this; it is the normal action when crossing a rope bridge after all - of course some of the more suspicious players may choose not to touch the ropes

)
Holding onto the ropes IMO would greatly improve stability, so I'd call it a +5 situational modifier to balance checks, so there's room to slip, and still hang onto the ropes.
All of these things you did. IMO your call was fine.
As a little aside, in situations like this (where something is more difficult than expected) the characters are rarely going to be oblivious to why; some descriptive aspect of the result of the failed roll can go a long way.
"As you step out onto the bridge it wavers underfoot, causing you to slip on the slick surface. Fortunately you manage to hold onto the ropes and regain your balance. It seems this crossing may be a little more difficult than you expected"
"The rogue lunges at you and misses. You raise your sword to strike him when he is off-balance only to realise to your horror that you were tricked, as he nimbly plunges his blade into your unprotected guts"