Like any other manure, animal or human, Rabbit has the potential of containing one or more disease pathogens. As long as that manure is put on the garden 90 to 120 days before harvest all indications are that greatly limits you exposure to those pathogens. So if you put that Rabbit Manure down now and don't harvest the Asparagus until May, 7 months away, there should be no great problem.
Far better is to properly compost any animal manure.

The sooner you put the bedding down the better.
I would compost the sawdust blend, if you are not going to till it in. I have never had a problem, but some people say it will crust over & cause water run off.

Thanks guys! NT

I've been using bunny mulch from a rabbit rescue place in MIchigan for 2 years. It is made of sawbust, poop pellets and straw. I completely mulched my hosta bed, roses, flowers beds and even some of my lawn this year. It was wonderful, I did not have any problems with crusting in this droughty year=watering only the hosta with a hose. I did have a few hay/straw seeds start to grow, but they were so easy to pull out.

For the lawn I seeded some areas that died because of the drought this fall, and then raked a (thin?) layer of bunny mulch over it. The grass seed grew well despite no rain,and my forgetfullness to water it daily.
I had already gathered bags of leaves from my neighbors to use in the vegetable garden as mulch.

when I used it as mulch for my garlic, I did throw some 12/0/12 on it for nitrogen. I will water the garlic next year, as the bulbs were really small when harvested in 7/12.

For the dahlias I mixed some bedding into their planting holes in the fall, but they did poorly because of the drought, and maybe lack of nitrogen because of the sawdust being mixed into the soil=their leaves were a good green color. I didn't water these plants in 2012, but may consider dragging the hose in summer of 2013 if the drought continues.

In the front yard this mulch was used at the base of the spreading junipers next to the grass. It was perfect for the mower to ride on and NO weeds. So that was less work in the 90 degree days.

In all my large flower pots, self watering or not, I put a 3 to 6 inch layer of this bedding in the bottom and a mulch layer of it on the top. The roots of the plants spread into it and I had the best looking pots ever-I did water them 3 x a week-from the cold pre-shower water that I saved in a pail in the bathroom.

My problem is that I have a difficult time putting those plastic bags in my Taurus without poking a hole in them and getting that mess in the trunk, despite having a tarp in there. In fact vacuuming my car is my chore for today. And the bunny place is a 30 minute drive from here, seldom do I find more than the 10 bags that I can fit into my car. Sometimes I only find one or 2 bags. I have 20 bags waiting for me for next spring-had 68 bags overwintering the previous year on the patio. Don't know how fast they will decompose as mulch though. The fresh cow manure and even aged horse manure is so smelly-this is not smelly nor messy.

I also used rabbit bedding, mine was poop, urin drenched hay/straw and newspaper. I simply buried it weekly in an ever expanding trench in clay soil of a perennial bed for many years, plants loved it.