The particle 'ní' precedes the verb in simple negation. When the verb is 'is', the verb is dropped.
With many verbs, there's a special form called the 'dependant' form, which is used when preceded by a particle, such as 'ní' (negation), 'an' (yes/no questions), &c. For 'tá', this is 'fuil'. The dependent form is generally affected by eclipsis (urú), so you'll typically see this as 'bhfuil'. So, if you wanted to say 'I don't have a bike', you'd say either 'Ní bhfuil rothar agat' or more typically 'Níl rothar agat' where 'Níl' is a reduced form for 'ní bhfuil'. If you wanted to say 'Do you have a bike', you'd say 'An bhfuil rothar agat'.
I think I'd better lay this down in more technical terms.
In Irish, 'ní' is essentially the equivalent of 'not' in English. However, it's also the negative form of 'is', so what's really happening in this circumstance is that 'is' is being substituted with 'ní', the negative form of the copula.
However, as the copula can be dropped completely in a good number of circumstances, it's often easier to think of 'ní' as simply meaning 'not' and that when you negate the copula, you omit it, thus leaving your with 'ní fear mé'.
'is' isn't like other verbs. The rules of how it behaves and is used are quite different from the rest.
I'm just looking at the wikipedia article on Irish syntax so I may be misunderstanding things, but it looks like 'ní' is a preverbal particle, which always* goes at the beginning of the sentence and negates the meaning of what follows.
*Only a Sith deals in absolutes. However, I didn't find a counterexample in the few searches I did.
ní is the negative participle used to negate every present tense verbs - ní ithim - "I don't eat", ní léann tú, "you don't read", etc. níl is a special case of this, because it is a collapsed form of ní fhuil, where fuil is the dependent form of tá (hence an bhfuil).
ní is also the negative form of the copula in the present tense - in this case it is not a particle, as it replaces is rather than just coming before it.