I would say the more important difference is the one between 以前 and 之前。The difference between 以前 and 前 follows from it.
(Bonus 1: to do yoga is better rendered with 练瑜伽)
(Bonus 2: to me, the sentence sounds better with a modal 了, as 开始 semantics inherently convey a change. native speakers might expand on this)
之前 expresses anteriority in time relative to something else. It can be used when describing event sequences in a time different than the present. It can be translated in English with "earlier, prior to".
Three months earlier, I (had) started doing yoga (relative to another given time)
以前 expresses anteriority relative to the present. It can be translated with "ago".
Three months ago, I started doing yoga (relative to the current time)
Though this distinction is quite faint. It's possible to find 之前 used just like 以前, and vice versa.
Now 前 alone could be an abbreviation of either of those, so its actual meaning is dependant on the context. Generally speaking, I would say there is no appreciable difference between 前 and 以前, except maybe that the former appears more frequently in writing.
A quick Google search:
site: xinhua.net "一个月前" yields ~7000 results
site: xinhua.net "一个月以前" yields ~3000 results
This is empirically true also for other combinations. Another example:
site: xinhua.net "一年前" yields ~65k results
site: xinhua.net "一年以前" yields ~3300 results