Yes, a bounce that goes into the basket would count as a successful goal. Anytime (except on a throw-in) a live ball goes through the basket, it is a goal, and it doesn't matter who, if anyone, threw the ball.
From the NCAA Men's Basketball 2013-14 and 2014-15 Rules, Rule 5 (Scoring and Timing Regulations), Section 1, Article 2:
Art. 2. A goal is made when:
a. A live ball that is not a throw-in enters the basket from above and remains in or passes through the basket; or
b. A free throw enters the basket from above and remains in or passes through the basket.
After a player bounces the ball, the ball is still live, meaning that any player could theoretically grab the ball and continue playing. So if the ball goes in the basket, the goal would count.
Kicking the ball in, even if it is easier for you, is not allowed (NCAA Rule 9, Section 7; NBA Rule 10, Section 4).