When I was an engineering intern at a manufacturing plant, I often felt uncomfortable exercising the privileges that my salaried engineering mentors told me I deserved but were denied to the union workers, such as parking at the more convenient office lot, entering through the front door, using the restrooms in the office area, and so forth. Once a union manager who didn't realize I was an engineering intern and thought I was union told me that I couldn't park in the office section of the lot. He was embarassed when my manager corrected him, but I was even more embarassed to be caught in the middle of a privilege dispute involving what seemed to me to be arbitrary class distinctions devoid of merit. Why should a 60 year old union manager have to park farther away than me? It made no sense to me, and I tried my best to be respectful toward the union workers and to avoid flaunting any privilege that went with my job.

As an intern, you should do as your manager tells you, and try not to complain about it, as you're actually quite lucky to have that opportunity. Do your best to get along with everyone and you'll be invited back or be given a better recommendation. Park the bike outside with good locks which you can probably leave on the rack at night if you want; if weather is an issue get a rain tarp or get a beater bike. You can also politely suggest improvements to the parking such as moving it to an area covered by a roof, if available, but don't get too frustrated if the suggestion is not accepted. As a 41 year old Senior Principal Engineer, I still can't get the building management that leases the space to our company to move the bike rack to an unused area under the roof.