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When I first learned 不, the accompanying pinyin was given as

bù (falling tone).

But I've also been doing Pimsleur Chinese lessons and there is the example

wo bú hùi shuo ying wen

and here the bu is pronounced with a rising tone.

My question is:

Is there a rule to when it is bù and when bù? Or does it depend on the speaker's dialect?

The rule about sandhi of 不 is:

1. It's pronounced in the original tone (the 4th tone) when being used alone or at the end.

规律一:单念或末尾时念本调。

不、就不、毫不、决不、都不、无不、何不、我偏不 

2. It's pronounced in the 2nd tone when being used before a 4th tone.

规律二：去声前念阳平。

不对、不算、不便、不怕、不必、不屑  不怕、不当、不定、不动、不利、不顺

3. It's pronounced in the 4th tone when being used before a tone other than the 4th tone.

规律三：非去声前念去声。

不听、不悲、不分、不蒙、不穿、不飞 不同、不曾、不行、 不纯、不回、不白  不美、不想、不好、不许、不准、不满

4. It's pronounced in the neutral tone when being used in the middle of words.

规律四：夹在词语中间变轻声。

想不开、起不来、行不行、大不了、对不起、大不大、谈不谈、拿不动、好不好、打不开

bù becomes bú when it precedes a falling tone.

I don't know -> wǒ bù zhī dǎo

I don't do -> wǒ bú zuò