Of a plant, to produce buds (which blossom into leaves or flowers). I'm so relieved to see that flower budding out—I thought I had killed it!
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
[for a flowering plant or tree] to develop buds. How early in the spring do the trees bud out around here? The trees bud out in early spring.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.