Difference between 以前 and 前 to indicate past time?

三个月以前我开始了上瑜伽课

三个月前我开始了上瑜伽课

三个月之前我开始了上瑜伽课

these three sentences have the same meaning.

三个月以前我开始了上瑜伽课 => 三个月以前我开始上瑜伽课了 or 三个月以前我开始了瑜伽课 is more fluent.

I think 以前 can be used as a word on its own and only refers to some unspecified time in the past, whereas 前 needs an accompanying phrase like 几天/几年 and has meanings not always associated with time.

Three months ago I started yoga classes.
我三个月前开始上瑜伽课。
三个月前我开始上瑜伽课。
Not so nice without a time:
*前我开始上瑜伽课。

前几天我碰到你丈夫了。
I ran into your hubby a few days ago.

以前我碰到过你丈夫。
I met your hubby before.

There isn't any essential difference between your two sentences. 前 or 以前 wouldn't affect the meaning.

However, the position of 了 can be improved. E. g.

三个月以前我开始上了瑜伽课

三个月前我开始上了瑜伽课

or

三个月以前我开始上瑜伽课了

三个月前我开始上瑜伽课了

You can also put 三个月以前 in the middle(after the subject 我):

我三个月以前开始上了瑜伽课。

If you want to be more factual, you can put:

我三个月前开始上的瑜伽课。

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".

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 "ago".

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.

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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