Brian tells Michelle he got the idea of calling on her in person, as he was driving through town in his car.

Brian - ... wrth yrru trwy'r dre yn y car jest rwan, roedd hi'n well gen i gael gair efo chdi wyneb yn wyneb...

'Wrth' in this context, means 'as' or 'while', and it's always followed by the mutated verb. So, 'Wrth yrru drwy'r dre' in this example means 'While driving through town...'. The same pattern is used for all tenses. You can tell which tense from the context.

'Wrth', with the meaning 'as' or 'while' occurs as a sort of refrain in the folk song 'Wrth fynd efo Deio i Dywyn' which means 'While going with Deio to Tywyn'. For those of you who are interested, here is the song in full.

Mi dderbyniais bwt o lythyr
Fa la la la la la la la la la la
Oddi wrth Mistar Jones o'r Brithdir,
Fa la la la la la la la la la la
Ac yn hwnnw roedd o'n gofyn
Fa la la la la la la la la la la
Awn ni efo Deio i Dywyn
Fa la la la la la la la la la la

Fe gychwynnwyd ar Nos Wener,
Fa la la ...
Dod i Fawddwy erbyn swper,
Fa la la ...
Fe gawn yno uwd a menyn
Fa la la ...
Wrth fynd efo Deio i Dywyn.
Fa la la ...

Dod ymlaen ac heibio'r Ddinas,
Bara a chaws a chwrw 'Ngwanas,
Drwy Dalyllyn yr aem i'n llinyn,
Wrth fynd efo Deio i Dywyn.

Dod drwy Aberygynolwyn
Ac ymlaen dan Graig y Deryn;
Pan gyrhaedd'som Ynys Maengwyn
Gwaeddai Deio, 'Dacw Dywyn.'

Os bydda'i byw un flwyddyn eto
Mynna'n helaeth iawn gynilo, -
Mi ga'i bleser anghyffredin
Wrth fynd efo Deio i Dywyn.

When Michelle asks Brian if he believes her, she says; 'Wyt ti'n fy nghredu fi?'

Whereas in English the words me, you, him, her, us or them follow the verb, in Welsh the reverse happens and they precede the verb.
For example 'Do you believe me? is Wyt ti'n fy nghredu i?' Literally,
'Do you me believe?'
Listen to some other examples:
'I believe you' is 'Dw i'n dy gredu di'. Literally, 'I you believe'.
'Dwi'n ei gredu e' - I believe him - I him believe
'Dwi'n ei chredu hi' - I believe her - I her believe
You mutate in exactly the same way that you'd normaly mutate after fy, dy and ei meaning my, your, his or her.