Both can work. In real terms, no native speaker would feel either was a mistake. I would go with speak as the verb is linked to used to and we follow used to with the base form of the verb: used to get.

The verb is to speak simple Present tense : speak( for an action still happening) simple Past tense: spoke ( for an action that has already happened) The structure of your sentence is a bit off instead of 'and' use 'that'(since you are referring to an action;getting excited) as for fast there is no need to use an adverb to describe it, the fact that you use fast by itself already say a lot. =>(in my opinion this is how your sentence should be): I used to get so excited that I ended up speaking fast in order to hide my nervousness. ( I used speaking cause it was an ongoing action while another action was going on 'getting excited' )

Both are possible. If you are considering the two parts of the sentence as separate statements, you would use 'spoke': the first part of the sentence would be "I used to get so excited" and the second would be "[I] spoke so ..." If both parts of the sentence are part of the 'used to' construction, you would use the infinitive 'speak': the first part of the sentence would be "I used to get so excited" and the second would be "[I used to] speak so ..." The second construction is neater and more logical. The words 'I used to' ( in square brackets above) are understood, so you don't need to repeat them before 'speak'.

Spoke is the past tense while speak is the continuous tense. Examples: "When I speak, I get nervous." "I spoke at a conference and was nervous." So in your sentence you should use "spoke."