Sounds like a crappy hotel with poor service standards.
Chances are the bellman was running a shuttle somewhere - I had friend who worked front desk at a fairly craptacular but "4 star" place and he had to drive the shuttle to places on occasion. They'd just grab anyone on staff, even maintenance, to run the shuttle around so they could claim they offered shuttle service to X, Y, and Z.
Honestly, "the problem was that your group was all checking in at once" is a remark that would cause me to resist backhanding the manager as someone trained extensively in customer service. Seriously, makes me want to take my white glove off and slap him across the face with it.
The problem is not that any number of people showed up at a particular time - it's that the hotel was understaffed and pretending to offer an amenity it does not. Real high end hotels have dedicated bell staff, always have someone working the luggage room, and more than enough carts - which are used by bell staff and thus retrieved, not just "take that if you need it."
There's not much you can really do about it - if they are a chain be certain to mention how crappy they were to the higher ups - but you're not wrong in being upset. It's not like you went to a cheap roach motel with outside corridors and a free breakfast and were shocked no one would help you with your bags. They have bell services, they should HAVE bell services.