Difference between 以前 and 前 to indicate past time?
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 &quot;earlier, prior to&quot;.

三个月之前我开始练瑜伽（了）
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 &quot;ago&quot;.

三个月以前我开始练瑜伽（了）
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 &quot;一个月前&quot; yields ~7000 results
site: xinhua.net &quot;一个月以前&quot; yields ~3000 results

This is empirically true also for other combinations. Another example:

site: xinhua.net &quot;一年前&quot; yields ~65k results
site: xinhua.net &quot;一年以前&quot; yields ~3300 results