Suppose you're in a situation where you have a formal/business relationship with someone, but the relationship has become more familiar over time. The other person continues to call you usted. How can you politely ask them to begin referring to you in the tú form? Is it ever inappropriate (by situation or geography) to ask to be referred to in the tú form instead of usted?
You can say in a cheerful tone:
Puedes hablarme de tú. (You may speak to me informally)
It might be helpful to precede the sentence with an encouragement word, like this:
¡Vamos! Háblame de tú. (Come on! Talk to me informally)
Please note that this applies particularly to Latin-American Spanish speakers. Some parts of Spain (and Argentina!) could be more conservative regarding the use of 'tú' and instead use the older 'vos'.
I understand that both of you are using “usted” with each other. In that case, in my opinion, it's inappropriate to address them using “tú”, even if it's to ask them to use “tú” towards you.
You should just politely propose that you start using “tú” between each other. Some options:
¿Por qué no nos tuteamos?
Ya podríamos tutearnos, ingeniero, ¿no le parece?
But if the situation is asymmetric, and you already treat them with familiarity, then use some of the proposals in the other answers.
Is it ever inappropriate (by situation or geography) to ask to be referred to in the tú form instead of usted?
Disclaimer: This answer could be very specific to a region but still answers this part of the question.
Indeed it could be inappropriate in some cases. I live in Colombia and, even when this is not the case in the whole country, I use "usted" in most cases. It's not always a matter of "formality" and distance, as I use it even with my family and close friends. It's a bit complex to explain because I do use also "tú", specially with women friends in spoken language, or in other contexts like this site, it's more natural for me to use "tú" when I write.
People from other regions use "tú" even in a work environment. For example my boss uses "tú" or "vos" (another informal variant) with me. I always use "usted" to reply to him, and it'd be a bit uncomfortable if he asked me to use "tú".
So I'd say that in most cases it'd be ok to ask someone to use "tú" with you, but there is also the possibility that some people (like me), depending on their region of origin, could feel a bit uncomfortable doing that.
In my opinion, the best answer here is that written by @MauricioMartinez. I will write a supplemental answer.
Before proposing or initiating a change (yes, as you get closer to the person, at some point it will often happen that "tú" feels right and "usted" no longer feels right, and things will morph without any fanfare), it's a good idea to observe how this person and the other people in this setting speak to each other while you're considering trying to change your footing with this person.
There are so many factors that can affect the other person's comfort level in using the informal with you:
region where you are interacting
region the person grew up in
the vibe in general (some historical periods tend more towards "tú" than some others)
your age and the other person's age, and the difference between the two ages
power difference between the two of you -- for example, if someone comes in to clean your house once a week, it is quite unlikely this person will ever "tutea" you, so if I were you I wouldn't even try
gender -- if you're of the same gender, tuteo becomes more likely
whether you and your colleague do things together outside work -- for example, if you help this person carry a heavy sofa up to a second story apartment, you will probably shift into tuteo pretty quickly
whether one or both of you are from the developed world such as US or Europe -- people are more likely to use "tú" with gringos
I have seen relationships in which the forcing or pushing of "tú" on another person is part of a bullying situation.
A gentle way of coaxing the relationship over into the "tú" realm is to introduce a third person into the mix. For example, let's say you have two colleagues, A and B. You are on "tú" terms with A, but not with B yet. If you then find yourself (or arrange to find yourself) in a reasonably extended conversation with both A and B, and A and B are already comfortable tuteándose, then it will be pretty effortless to morph over with B. (Assuming there are no gender or power factors that would override other considerations.)