Enclose the password in double quotes (") to handle special characters. Use {{ to escape the { symbol in the password.
"
{{
{
Try bcp "Database.dbo.Table" out "outputfile.txt" -S Server -U Username -P "PasswordWith{{" -c.
bcp "Database.dbo.Table" out "outputfile.txt" -S Server -U Username -P "PasswordWith{{" -c