Ridership is broadly a combination of five factors:
Reach of Service: Does public transit get me to where I need to go, or at least close enough as to be convenient? If not, then it is of no use to me.
Speed of Service: Do I reach my destination in a reasonable amount of time, compared to other potential transit methods? If it takes an hour to get to work by bus but only 20 minutes by car, then I'm going to drive.
Frequency of Service: How long do I have to wait for the bus/train to arrive? If missing my train means I only have to wait another 7 minutes then fine, but if it means I'm waiting 30 minutes and would be late for my shift, that's a risk I may not be willing to take.
Reliability of Service: Is the service schedule kept to reasonably well with trains/busses reaching their destination generally around the posted time? If the bus routinely runs 10 minutes or more behind, or worse sometimes doesn't even show up, I can't risk it as a commuting option.
Safety of Service: Do I feel reasonably safe from harm on public transit? This is particularly an issue for solo female riders. Even if driving is less convenient I may still choose to do it if I feel unsafe or are actually a victim of a crime on the public transportation system.
If your public transit system is fast, frequent, reliable, safe, and gets people where they need to go, they will ride it regardless of cost unless you're talking astronomical commuter line rates (ie: >$10 per ride). Likewise if your system is slow, infrequent, unreliable, unsafe, and doesn't get people where they need to go, you're not going to get many riders even if you drop fares to zero.
None of which is to argue against eliminating fares in a vacuum, but you need to weigh the trade-offs. Many public transit systems rely on fares to operate, and if you compromise any of the factors I listed in the process of eliminating fares it's going to reduce ridership, not increase it, even as the price to ride drops.