The proper distance depends on the size of the shrub in question. Hellebores like a rich deep root run. You can humus to the soil at the planting point but if the shrub is close by and has surface roots, it will quickly take up the nutrient. If your 'Burning Bush' is Kochia then I guess it's a fairly low shrub and the roots probably only extend 18" or so. So I would plant beyond that distance. You could also cut off some of the shrub root at least to get the Hellebore established, but fresh rich soil and pruned roots will probably just result in a lot of new growth.

Cheers Greenmanplants