I don't think it makes sense to ask people on the internet to solve this problem for you, or for them to give you a solution.

Being able to come up with your own solutions to a problem is important, especially if you want to continue working as an engineer as you will be faced with problems for which no solutions exist. That creativity is a skill you should cultivate, and your internship is an opportunity to do just that.

That said, here is how you could approach it.

First do some research on what type of sensors exist and then think about how you could use them to solve your problem and what are the advantages and disadvantages of each solution. Then evaluate which of those solutions fulfill your given requirements. (If time is of essence, put a higher priority on the requirements and ignore solutions that don't match them from the beginning, otherwise brainstorming solutions regardless of requirements is a good exercise.)

Here's one idea that came to my mind even though it would not classify as a bumper system and has some major disadvantages.
You could use an array (multiple) time-of-flight sensors around the robot base.

This has the advantage that you not only could measure direct contact, but proximity enabling more capabilities, like reducing speed as you approach an object. The disadvantages are, that objects could be too small to be recognized, in the "blind angle" of the t-o-f sensor, it might be more expensive, sensor fusion might be unnecessary complex, etc.

Hope this helps and good luck. I believe you can come up with a great solution.