Some bottlebrushes like quite moist soils but are still drought tolerant while others cope with dry conditions well. Bottlebrushes flower with the production of new growth, so best flowering occurs when the bush/tree is pruned after flowering. Cut off the old flowers and seed pods back to green leaves. Some recover very well from hard pruning into bare wood. If you know the name of your bottlebrush there may be more info available. Some new growth is not frost hardy so don't prune too much at this time of the year.

Your bottlebrush tree is probably just having a rest for winter. If it looks healthy, nothing bad will happen if you ignore it completely - but it will flower all the better if you prune it as Mallee suggests. You don't want to prune in spring, as you would be cutting off the flowering material. I would probably prune it now despite the frost risk, so long as the bits you want to cut off are a decent distance from the ground, and the tree isn't situated somewhere where the frost pools. Next year, though, it would be better to prune it as the flowering season finishes. (Cut back to just behind the flowers). Sometimes I prune bottlebrushes twice a year. Getting to the job as soon as the first flush of flowers finishes can encourage a better second flush.
Even if you don't know its botanical name, can you describe your bottlebrush for us? There are SO MANY different kinds! Tell us about the flowers, the bark, the trunk diameter, the age of the plant ....
Trish

Mallee and Trish, Thank you for your clear and helpful responce. I don't know the history of the tree as it was here when I bought the house 16years ago. Your advice makes a lot of sense and I am sure,when I put it into practice,it will be back to its bloom'n' self. Thanks to you,I have the confidence to know what I am doing now.

I have a beautiful Bottlebrush tree in my back yard in Houston Texas. After Hurricane Ike the tree was pushed over. I have secured it but it is not going to make it in it's present location. I would like to move it up front but need to know how this should be done, if at all. Can someone please help me?

I have collected seeds off a bottle brush tree and can't find how to propagate them. They are from last years flowers and very hard. I would be grateful for any information and advise.

Robert, there are LOTS of different bottlebrush trees - literally hundreds of species. They come from all sorts of environments from coastal swamps to semi-desert, and have the variation in root type that you would expect. Some are long-lived species, others have more or less had it after thirty years or so. It would be much easier to make an intelligent comment on your move-the-plant question if we know both what kind - even approximately what kind - of bottlebrush you have. I would also help if we knew how big it is, and what kind of soil you had.
Tbgardens, what you probably have are not "seeds" but seed capsules, which would be full of very fine seed. Put them in a warm dry place, in a paper bag, and see if seed comes out after a few weeks. (If not, an hour or so in a low oven may help). The seed is very easy to grow.
Trish