On the assumption that your climate there is not dissimilar from ours, plants like busy lizzie are summer bedding, and should not be planted outside before the end of May. If you order plug plants, you will need to keep them either indoors or in a greenhouse while they grow on until late May.
Your bulbs will be fine snuggled in under the snow, they will appear when the time is right.

Hi Detta, I can't see any reason for your bulbs not flowering, there are some pictures on here where crocus have actually flowered under-in the snow. Please don't be tempted to plant out any plugs until the complete risk of frost has gone, which is unlikely in March. I keep mine in a greenhouse, temperature controlled, bring them on and hardy them off.

Snap Bamboo !

mine that flowered under the snow were autumn crocus and just got covered by the nov snows.

Hi Detta, for colour in March from plug plants, you'd need to plant something like winter flowering pansies in the autumn. I find they mostly stop flowering in winter, but do produce flowers in late autumn and start again in early spring. I have some that are about 16 months old that are flowering again, having self seeded (welcomed by me) in summer as well.
Other plants for winter colour can be found if you click on "W" at the bottom of any page. I'd recommend Cyclamen coum and primroses / polyanthus as well.

And I'm sure your bulbs will all be fine! :-)