Ask Mr. Smarty Plants

The bottle brush tree is native to Australia and New Zealand where its red blossoms appear appropriately at Christmas time. Since our expertise is limited to plants native to North America we do not know its effect on plantings near it. Maples are relatively shallow rooted and native plants can be grown successfully under them taking care to not disturb the tree's roots. Native plants are preferable as they are more likely to be adapted to living under the trees in their area. 

That said, your options are varied and wide, so much so you may want to peruse our Plant Database yourself rather than be limited to our suggestions. I like using the Combination Search where you will indicate shade for light requirement and dry for moisture for your Texas location. Then your choices are more complicated as you may select a sub-shrub, grasses, ferns or herbs (flowering species) depending on the landscaping effect you prefer. I've selected a few below you may want to consider.

Pteridium aquilinum (Western bracken fern) Ferns have deep roots and may spread widely in landscaping. They are ideal in a dry, shaded location. Walk through a wild woodland and note how prolifically ferns populate the forest floor.

Pteridium aquilinum var. pseudocaudatum (Bracken fern) This is a variant of the above listed fern. In spring, ferns produce edible fiddleheads, actually the growing tips of the fronds.

Aquilegia canadensis (Eastern red columbine) The native columbine produces showy flowers from February to July and is an easy, graceful addition to any landscape.

Apocynum androsaemifolium (Spreading dogbane) Dogbane is a bushy, sometimes aggressive plant with fragrant flowers. The milky sap may irritate skin.

Calyptocarpus vialis (Straggler daisy) Perhaps you prefer a groundcover in this site. This plant tolerates foot traffic and can proliferate to the point of being a pest. For some sites, that  enthusism to spread is appreciated.

Polygonatum biflorum (Smooth solomon's seal) Solomon's seal does particularly well at the base of trees. It has graceful arching stalks and bell-like white flowers.

Ruellia drummondiana (Drummond's ruellia) Also called the wild petunia, this native plant produces purple blossoms from June to November in shade or part shade.

Symphoricarpos orbiculatus (Coralberry) The coralberry is a favorite (and doing well under my maple tree). This shrub has insignificant white blossoms that develop beautiful red berries which persist through winter. It self propagates from its own stems where they touch the ground.

Pteridium aquilinum

Pteridium aquilinum var. pseudocaudatum

Aquilegia canadensis

Apocynum androsaemifolium

Calyptocarpus vialis

Polygonatum biflorum

Ruellia drummondiana

Symphoricarpos orbiculatus