Hardwood non toxic trees would be the first choice. Finding sone DW from a river may be a good choice.
A dead tree or even shrub preferably one not in the grass in case of weed and feed which is systemic and can be taken up into the shrub or tree, also in an area that isn't sprayed by the landscapers/ground keepers or next to a agricultural field where they get over spray and drift from herbicides and pesticides. You get the idea.
I even found a rootball section from a dead young tree which was an awesome find.
Soak it and add Prime to help neutralize toxic residue.
Also remember that the Betta has flowing fins and caution must be taken to sand down any sharp edges and avoid tiny pointy branches he can snag the tail or poke an eye or body in a startling situation.
also DW is available at the lfs
from the reptile section from reputable companies like zoo med, from ~$6.99 -14.99