What I would do...

Absolutely grab some of the partially broken down compost with the worms.

If you can shred the cardboard, that would be helpful. Paper by itself tends to clump, especially newspaper. Shredded cardboard helps break up the clumps.

Put in just a handful of the scraps. Freeze the rest.

The worms will eat the partially broken down compost at first.

Yes, I'd agree with S bryce.
The OSCR bin is a great design with loads of air coming in at the bottom so you shouldn't have too much of a problem with smells. I'd grab as much of the broken down compost as you can get, use some as bedding and pre-mix some through your food scraps to speed up breakdown.
In my experience you can't go far wrong if you don't add more than about a half an inch of food, spread over a third to a quarter of the surface of your bin twice or three times a week. Then add some damp (not really wet) bedding over the scraps to stop flies getting at it.

cathd66's suggestion works in a well established bin, but is too much food for the first two or three months.

But it depends on what you feed them. I have a lot of onion peels and cabbage cores to feed my worms. If I covered 1/3 of the bin 1/2 inch thick, it would stink for days. Right now I have about 1/4 of my bin covered 1 inch deep in horse manure. The worms are lining up for seconds and thirds at the all you can eat buffet, and there is barely any smell.

Thanks for the replies. I just added some food to the bin. I took a few carrot ends, some celery tops and bottoms, some lettuce, a little corn, an apple core, and a coffee filter and grinds. It was maybe two handfuls tops. I put it in one of the corners. I then took the worms and compost I got from the community garden and dumped it over the food and sort of spread it out so the dirt/compost would get in with the food. I then covered it with a few inches of newspaper that I soaked and squeezed until there was very little water if any dripping off of it. I am going to try my best to not open the bin for a few days. I didn't realize how much scraps I collected from one evening of cooking. It makes me want to go out and buy three more bins! Now it is time to freeze my left over scraps. I never thought I would say that.

What you have done sounds perfect. I have fed carrot, celery, lettuce and apple, and found them all to be great foods for the worms. They all break down quickly and don't smell while they break down. The hard part will be leaving the bin alone for a couple of days.

It will take about 4 days before the worms show much interest in the kitchen scraps, maybe longer in a brand new bin. In the mean time they will eat the compost.

Just be sure not to feed them again until all the scraps are gone. The broken down compost is great too.

Well, after cooking last night and cleaning up. I managed another bag of scraps for the freezer and some more waste for bedding. It is really amazing to think that one day, I will be able to feed it all to my worms. All this got the better of me and I just finished up making my second OSCR,jr. It is even better than the first. Of course only will time will tell how the worms like it. I haven't told my wife about my worm addiction yet. I hope she takes it well. :)

"cathd66's suggestion works in a well established bin, but is too much food for the first two or three months.

But it depends on what you feed them."

Yes I should have specified, a good mix of foods. I find that with a well ventilated bin, ie air coming from below as well as from above, you can get away with half inch feed/ one inch bedding per week. In fact I've done this for a couple of months without worms and just relied on normal composting without developping smells (one of my precomposting experiments!). When worms were finally added, they went mad for the partially composted mix.