As everyone knows:
one basis point is 0.01%, and one cent is 0.01% too.
The difference is that we typically use cents when we refer to an upfront price, and use bips when we refer to a rate (in a swap for example).
So a trader may ask:
“what is 3 bps worth upfront?”
which means you should change the rate by 3 bps (in the direction that makes the PV of the trade positive to your trader) and see how much the PV changes. If the change in PV is 0.15% then you’d reply:
“3 bips running is worth 15 cents upfront”.
[ By the way, you could have said: “3 bips is worth 15 cents”, but the two little words running and upfront make sure it is very clear what you mean, and it is always important to minimize the chance of being misunderstood. ]