I didn’t “bribe” mine, but I did tie certain expectations and rewards to getting things done that should be done. For example, allowance was tied to doing chores. With chores, there was some choice, and they were welcome to trade with each other. If there was something expensive they wanted, they were welcome take on extra work in order to get it.
Things like dance lessons, tennis, after school activities that cost money were earned by getting good grades. However, responsibility to completing school work and studying came before anything else and they were not bribed for doing their school work. The expectation was that they would work hard, and do their best work every day, and correct their mistakes. Studying is the work of children. I checked homework (because they asked me to) all the way through high school, and they corrected their own mistakes. Even in college, I’m sometimes asked to proof papers.
We didn’t have a lot of “stuff” that were distractions in the house. One television, in a central location off the kitchen, no games systems, computer was in a shared location, etc.
Money and privileges are motivators for adults at work, and I see nothing wrong with kids being incentivized for certain things. But you do have to choose your priorities, because there are conflicts. Which comes first—school, chores or sports/extracurriculars? We all made sacrifices for schoolwork coming first, in terms of no one watched television until homework was done, paying for tutors and academic enrichment programs, providing access to books and learning materials, talking about what they were learning and sometimes supplementing the material.
ADD: When they got older, I would give them a list of things to do, and a time by which I expected them to be completed, with some negotiation as to the “when” factor. Asking a teen to block out some time to do certain things requires being respectful of their own time, seemed to yield better cooperation, because the issue then became about them honoring their commitment, and not about me trying to control them.