I do not know your overall skills to rate if it is over your head, but if you have never hiked on a glacier at all and are looking at doing Bomber Glacier (and I assume want to hike through the bomber as well) then you should go with some experienced glacier hikers.
I would guess that you would likely be fine with micro spikes and lightweight mountaineering axes (less concerning of the 2), if you had experience, I would hesitate to go alone on any glacier with no experience, and such equipment.
Year round the glacier has snow on it and every month sees snow there. Fresh snow obscures the safest routes and can hide cracks, crevices and worse.
You should contact the mountaineering club of Alaska. Even if they do not have a well-timed trip through the area they ill likely know of people that are looking for any excuse to ike that area again at a time that will likely work with you.
What route are you considering? When I hiked it I went through Mint Glacier trail, camped overnight near Mint Glacier Hut, then hiked over Backdoor Gap the next morning. I was hoping for firm snow/ice in the early hours of the day, but I did not count on clouds covering the view completely as I looked across the gap. I waited for about two hours for the clouds to dissipate and then proceeded onward. It was glorious but it was a glacier.
You have to be careful out there. Oh yeah, get some real strap on crampons. Â You will not regret it.