Be very careful about showcasing anxiety in dialog. People love using an excessive amount of "ums" and "ahs" for this along with outright stuttering, but in my opinion this very often comes across far more like a speech disorder than nervousness. Conflating stuttering with excessive nerves and anxiety is both inaccurate and offensive, and as someone who stutters I wish writers would leave my disability alone if they can't write it with the respect it deserves.
Which isn't to say that there's no place for "um" and "ah", but try to make sure there's a reason for the pause. Is the character suddenly thinking the better of what they're saying? Do they trail off halfway through or start contradicting what they said earlier? That's a good reason for someone to pause. Are they trying to build up to something they think the other person might take offense at? Maybe - but in that case I'd also expect a lot of circumlocution, talking around the issue, softening, preemptive "this is just my opinion"/"maybe I have this wrong"/etc., and the "ums" and pauses coming as they change tracks. If you just litter their speech randomly with filler words and pauses, that... again, that's how someone with a speech disorder talks. Here be dragons.
I also think this is a very... low-level, for lack of a better word, place to start trying to depict anxiety. I'd first start off with how it influences the character's motivations and actions. For instance, an anxious or nervous character might be very indecisive or risk-averse. They might be constantly jumping to the most negative possible consequence of any action they could take, or have a heightened sense of potential danger, or a disproportionate fear of negative outcomes where e.g. failing at something is considered world-ending, or similar. If they're shy, social situations could be classed as a "dangerous situation", and any sort of potential embarrassment considered a disastrous outcome to be avoided at all costs. At the same time, they might be very unsure of and mistrustful of their own instincts and reactions, i.e. easy to influence and talk into things (and sometimes end up talking themselves into things) because they know their fears are often irrational and are therefore primed not to take them into account.
Once you have that in mind, you can figure out how your character is going to act in a given situation, what sort of decisions they will make, how they will react to things, what their emotional responses will be like. At that point the lower-level depictions like dialog and body language should hopefully come more naturally. As a bonus, they'll be more appropriate to context! If you focus too much on the lower-level depictions, you'll be primed to write your shy/nervous/anxious character the exact same way regardless of whether they're at a party with lots of people they barely know and really want to impress or whether they're at a one-on-one lunch with their best friend since childhood, which doesn't come off realistic at all.